Appendices - Physics
To avoid long and involved explanations, the objective of
these appendices is to develop deeply what is stated in the main pages: data,
explanations and formulation needed for a deep theoretical and practical
knowledge.
So, in the main pages the subject will be developed in the
minimum extension to be clearly understood with references to the appendices
which conclusions will be assumed there.
Física. Curso teórico práctico de fundamentos físicos de
la ingeniería ISBN 84-7360-187-4. Biblioteca Vázquez Montalbán
1
Ciencia y técnica
1.1
Experimentación e ingeniería
1.2
Hipótesis y teoría
5
Sistemas de unidades
5.1
Observables, magnitudes y cantidades
5.2
Análisis dimensional
6
Trigonometría
6.1 Ley de
cosenos
6.2 Ley de
senos
7
Sistema de referencia y de coordenadas
7.1
Coordenadas cartesianas rectangulares
7.2
Coordenadas cilíndricas
7.3
Coordenadas esféricas
8
Álgebra
8.1
Escalares
8.2
Números complejos
8.3
Vectores
8.3.1
Tipos
8.3.1.1
Libres, Deslizantes, Ligados o fijos
8.3.1.2
Polares, Axiales
8.3.2
Expresión
8.3.2.1
Versores
8.3.2.2
Coordenadas
8.3.2.3
Cosenos directores
8.3.2.4
Longitud o módulo y Norma
8.3.3
Operaciones
8.3.3.1
Suma y relación de Chasles
8.3.3.2
Producto por un escalar
8.3.3.3
Producto escalar.
Ángulo de dos vectores.
8.3.3.4
Producto vectorial
8.3.3.5
Producto mixto
8.3.3.6
Doble producto vectorial
8.3.4
Cambio de coordenadas
8.3.4.1
Traslación de ejes: las componentes no varían
8.3.4.2
Rotación de ejes: cambian las componentes, pero no el módulo
8.3.5
Momentos
8.3.5.1
Momento de un vector deslizante respecto de un punto
8.3.5.2
Momento de un vector deslizante respecto de un eje
8.4
Torsores
8.5
Fasores
8.6 Kets
9
Geometría
9.1
Ecuación de una recta
9.1.1
Ecuación vectorial
9.2
Ecuación de un plano
9.2.1
Ecuación vectorial
9.3
Representación vectorial de una superficie
10 Geometría
de masas
10.1 Centro de
masas
10.1.1 Teoremas
de Guldin-Pappus
10.2 Momento de
inercia
10.2.1 Teoremas
de Steiner
11 Funciones
vectoriales
11.1 Derivada
de una función vectorial
11.1.1 En
coordenadas cartesianas
11.1.2 En
polares
11.1.3 En
esféricas
11.2 Reglas de
diferenciación
11.3
Integración vectorial
12 Campos
12.1 Escalares
12.1.1
Gradiente
12.1.2
Superficie equipotencial y Línea de fuerza
12.2
Vectoriales
12.2.1
Rotacional
12.2.2
Divergencia
12.2.3 Flujo
12.2.4
Circulación y
12.2.5 Función
potencial
13 Operadores
13.1 Giro de
180º (-)
13.2 Giro de
90º (i)
13.3 Nabla
14 Cinemática
de un punto
14.1
Trayectoria
14.2 Vector
tangente unitario a la trayectoria
14.2.1
Curvatura y radio de curvatura
14.2.2 Vector
normal principal
14.3 Velocidad
14.4
Aceleración
14.4.1
Aceleración tangencial y normal
14.5 Algunos
movimientos
14.5.1
Movimiento uniforme 
14.5.2
Movimiento variado uniformemente 
14.5.3
Movimiento de rotación
14.5.4
Movimiento helicoidal
14.5.5
Movimiento periódico
14.5.6
Movimientos armónicos (vibraciones y ondas)
14.5.7
Movimiento variado no uniformemente 
15 Cinemática
de sistemas
15.1 Traslación
15.2 Sistemas
indeformables
15.3 Campo de
velocidades de un sólido
15.4 Campo de
aceleraciones de un sólido rígido
15.5 Movimiento
plano del sólido rígido
16
Composición de movimientos. Movimiento relativo
17 Dinámica
del punto material
17.1 Fuerza
17.1.1 Peso o
fuerza gravitatoria
17.1.2 Fuerzas
de rozamiento
17.1.3 Fuerzas
de deformación elástica
17.1.4 Fuerzas
ficticias
17.1.4.1 de
inercia
17.1.4.2
Centrífuga
17.1.4.3
Coriolis
17.2 Trabajo y
energía.
17.3 Fuerzas
conservativas.
17.4
Conservación de la cantidad de movimiento.
18 Dinámica
de un sistema de partículas
18.1 Centro de
masas
18.2 Cantidad
de movimiento
18.3 Momento
cinético
18.4 Sistemas
de masa variable
18.5 Dinámica
del sólido indeformable
18.6 Rotación
de un sólido rígido sobre un eje
18.7 Rotación
de un sólido rígido sobre un punto. Giróscopo
18.8 Movimiento
plano del sólido rígido
19 Estática
19.1 Estática
del punto material
19.2 Estática
del sólido rígido
19.3 Equilibrio
19.4 Estática
de hilos.
19.4.1 Polígono
funicular.
19.5
Estructuras articuladas planas
19.6 Esfuerzos
en barras
20
Elasticidad
20.1 Esfuerzo –
deformación
20.2
Deformación longitudinal (tracción y compresión)
20.3
Contracción transversal. Coeficiente de Poisson
20.4
Compresibilidad uniforme. Elasticidad de volumen
20.5
Cizalladura. Módulo de cortadura. Elasticidad de forma
20.6 Torsión
20.7 Constantes
elásticas
20.8 Energía de
deformación
20.9 Flexión
20.10 Esfuerzos
y fracturas
21 Mecánica
de fluidos
21.1 Estática
de fluidos
21.1.1 Líquidos
no miscibles
21.1.2 Prensa
hidráulica
21.1.3
Manómetros
21.1.4 Fuerza
hidrostática sobre superficies sumergidas
21.1.5
Principio de Arquímedes y estabilidad
21.1.6 Tensión
superficial
21.1.6.1
Capilaridad
22 Dinámica
de fluidos
22.1 Ecuación
de continuidad
22.2 Ecuaciones
de Euler y Bernouilli
22.2.1 Tubo de
Venturi
22.3 Pérdidas
en conducciones
22.4 Dinámica
de fluidos viscosos
23
Termodinámica
23.1
Temperatura
23.2 Gases
reales
23.3 Dilatación
térmica de sólidos y líquidos
23.4 Calor
específico. Calorimetría
23.4.1 Fusión y
vaporización
23.5 Trabajo en
termodinámica
23.6 Primer
principio. Conservación de la energía
23.7 Segundo
principio. Dirección de la transferencia espontánea de energía
23.8 Ciclos de
energía
24 Fenómenos
de transporte
24.1 Difusión
24.2
Transferencia de calor
25
Higrometría
25.1 Atmósfera
terrestre
26
Vibraciones y Ondas
26.1 Movimiento
armónico simple
26.1.1 Muelle
26.1.2 Péndulo
simple
26.1.3
Movimiento armónico de rotación
26.1.4 Péndulo
físico
26.2
Oscilaciones no armónicas
26.3
Vibraciones amortiguadas
26.4
Vibraciones forzadas
26.5 Fenómenos
ondulatorios
27
Electrostática
27.1 Ley de
Coulomb
27.2 Campo
eléctrico
Flujo de campo eléctrico. Teorema de Gauss
27.3 Potencial
electrostático
27.4
Dieléctricos
27.5 Inducción
electrostática
27.6 Capacidad.
Condensadores
28
Electromagnetismo de la materia
28.1 Estructura
eléctrica de la materia
28.1.1
Orbitales electrónicos
28.2
Propiedades magnnéticas de la materia
28.2.1
Diamagnetismo
28.2.2
Paramagnetismo
28.2.3
Ferromagnetismo
28.2.3.1
Histéresis
29
Electrocinética
29.1 Corriente
eléctrica
29.2
Resistividad y conductividad
29.3 Ley de Ohm
29.4 Teoría
elemental de circuitos
29.4.1 Leyes de
Kirchhoff
29.5 Corrientes
variables
29.5.1 Carga y
descarga de un condensador
29.5.2
Conducción en líquidos
30
Electrodinámica
30.1 Movimiento
de una carga en un campo eléctrico
30.1.1 Campo
longitudinal
30.1.2 Campo
transversal
30.2 Fuerza
magnética sobre carga en movimiento
30.2.1
Trayectoria plana
30.2.2
Trayectoria no plana
30.3 Fuerza
magnética sobre una corriente
30.4 Efecto
Hall
30.5 Campo
magnético
30.5.1 Creado
por cargas en movimiento
30.5.2 Creado
por circuitos
30.5.2.1 Espira
30.5.2.2
Solenoide
30.5.3
Interacción de dos corrientes paralelas
30.5.4 Flujo y
circulación del campo magnético
30.5.5
Interacción campo-espira
30.5.6 Fuerza
electromotriz inducida
30.5.7
Generador de corriente alterna y dinamo
30.5.8
Autoinducción
Energía asociada
30.5.9
Inducción mutua
31 Circuitos
de corriente alterna
31.1 Efecto
Joule en corriente sinusoidal
31.2 Intensidad
y tensión eficaz
31.3 Circuito
con resistencia
31.4 Circuito
con autoinducción
31.5 Circuito
con capacidad
31.6 Circuito
RCL. Circuito resonante
31.7 El
transformador
32 Ondas
electromagnéticas
32.1 Ecuaciones
de Maxwell
32.2
Cuantificación del campo electromagnético
Physics concepts
Position
Coordinates: A set of numbers used to locate a point along a line or
space.
Distance
Trajectory
Mass
The mass of an object is a measure of resistance to change its motion
(inertia). It is defined as equal to force divided by acceleration
It is also a measure of its capacity to pull or to exert attraction force to
other bodies (gravitation).
Change
Physicists study how things happen. They have discovered that some magnitudes
remain invariable. In a isolated system, for example, the energy remains the
same for ever. But usually they need to study how they change. The Greek letter
capital delta (Δ) is used to denote change in some
quantity.
Speed and velocity
The speed is a magnitude without direction defined as the rate at which
distance is covered (speed = distance/time) and measured in m/s, km/h, cm/s,
Mph, etc
Velocity is a magnitude with direction defined as the speed in a specific
direction.
Acceleration and Gravity
Acceleration (a) is the rate at which speed or velocity change. a = v/t (m/s2)
Gravity (g) is the acceleration (pull) caused by of the Earth to all the
surrounding objects. g = 9.8 m/s2
Work
Work is the net force on an object times the distance through which the
object moves. W = F·d (N·m
or Joules (J))
Work of gravity W = mg·h
The Joule is a unit of work (or energy); one joule is equal to one Newton·meter,
also one watt·second.
Energy
Energy is the capacity to do work (N·m)
Kinetic Energy is the capacity to do work by virtue of the body's motion (KE=
½ m·v).
Kinetic energy.
Potential Energy is the stored energy. It potentially has a capacity to
produce work but needs some condition to happen.
Potential Energy of Systems: Gravity (PE = mgh). Spring (PE = ½ K y).
Gas in a bottle (PE = ½ V/Po p).
String (PE = ½ 2T/L y)
Power
Power is the rate of doing work; equal to work or energy divided by time.
P=W/t (J/s or Watts (W))
The Watt is a unit of power equal to one joule per second.
Physical World
Humans have always been curious about the world around them. The world has an
astonishing variety of materials and bewildering diversity of life and
behaviour. The inquiring and imaginative human mind has responded to the wonder
and awe of nature in different ways. This human endeavour led, in course of
time, to modern science and technology.
Measurement and Experimentation
The goal of physics is to provide an understanding of nature. This
understanding is verified experimentally. Experiments involve the measurement of
various quantities and a great deal of effort has gone into making these
measurements as accurate and reproducible as possible. Basic standards of
measurements have been established and units agreed upon internationally.
-
-
-
Units. International System of
Units (SI)
-
-
Estimation & Approximation
-
Accuracy
-
Significant Figures
-
Errors
-
Measurement Procedure
-
- Vernier Callipers
- Micrometer Screw-Gauge
- Longitud
-
It is the shortest distance between two ends of the body. For measuring
lengths, two methods can be employed, namely direct method and indirect
method. Direct methods are employed for measuring small lengths by
comparing such lengths or distances with an approved standard of length
viz. vernier callipers, screw gauge and so on. For long, atomic and
astronomical distances, indirect methods are used.
Some objects have a wide range of lengths in the universe.
By Avogadro's hypothesis, the actual volume occupied by the atoms in
one gram of a substance is 2/3rd of the volume occupied by 1
gram of the substance.
A solution of known concentration of oleic acid in alcohol is prepared.
Let moon be the astronomical object of diameter D. Let E be the point
on earth's surface.
Let AB be an electric pole, standing upright, on the ground. Let the
point C be the observation point i.e., the observer standing.
AB and CD are two mirrors fixed, as in the diagram, parallel to each
other and facing each other, i.e., the reflection on CD is seen on AB. A
small telescope and a vernier travelling over a scale, graduated in
degrees, constitute the sextant.
Let PQ be the symbolic representation of the mountain (h), inaccessible
for direct measurement. Let A and B be two points of elevation subtending
angles q1 and q2 of the top of the mountain at P.
PQ, the width of the river= W. AB, the known distance= x
Ultrasonic waves are transmitted through the ocean and if on its path
any submerged objects are encountered, then as per law, the waves are
reflected back to the origin.
-
-
It is the mass of a body measured, when it is in translatory motion, by
the application of external force other than gravity.
In 1967, the atomic clock was adopted, choosing caesium-133 atom, which
emits electromagnetic radiation of a precise and unvarying frequency,
corresponding to the transition between two hyperfine levels of the ground
state.
-
-
-
-
-
Measurement Instruments
Motion
In the physical world, one of the most common phenomena is motion. The branch
of Physics, which deals with the behaviour of moving objects, is known as
mechanics. Mechanics is further divided into two sections namely Kinematics and
Dynamics. Kinematics deals with the study of motion without taking into account
the cause of motion, while Dynamics is concerned with the cause of motion,
namely force. This chapter covers only the different aspects of motion without
considering the cause of motion.
-
In the physical world, one of the most common phenomena is motion. The
branch of Physics, which deals with the behaviour of moving objects, is known
as mechanics. Mechanics is further divided into two sections namely Kinematics
and Dynamics. Kinematics deals with the study of motion without taking into
account the cause of motion, while Dynamics is concerned with the cause of
motion, namely force. This chapter covers only the different aspects of motion
without considering the cause of motion.
-
-
Imagine you are travelling in a moving train. Do you observe any change in
your position with respect to your co-passengers? Is there any change of scene
you view through the window? The change of scene indicates that the train is
moving. That is, an object is said to be in motion if it changes its position
with respect to its surroundings in a given time.
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In translatory motion the particle moves from one point in space to
another. This motion may be along a straight line or along a curved path. The
motion along a straight line is called rectilinear motion.
-
-
The distances covered by car A and car B with respect to time is given
below.
-
In an athletic meet different participants start running at the same time
and cover the same distance. The person who takes the minimum time to cover
the distance will be judged as the winner.
-
Mr.X is traveling from terminus A to terminus B in a bus and records his
observation.
-
Velocity is defined as the distance covered by a moving object in a
particular direction in unit time or speed in a particular direction.
-
All of us know that a car moving on road does not have a uniform velocity.
Either the speed or the direction changes. Whenever a vehicle is speeding
i.e., when the speed is increased we say that the vehicle is accelerating.
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Imagine that two athletes Tom and Harry are running with a uniform speed of
5 m/s on a straight line and circular track respectively. For a layman both
Tom and Harry are moving with uniform velocity but for a physicist only Tom is
running with uniform velocity because there is no change in his speed and
direction of motion.
-
In the example discussed under the topic uniform and non-uniform motion we
have classified motion along circular track as an example of non-uniform
motion.
-
The variation of velocity with time can be represented graphically to
calculate acceleration exactly like we calculated speed from distance-time
graph.
-
The variable quantities in a uniformly accelerated rectilinear motion are
time, speed, distance covered and acceleration. Simple relations exist between
these quantities. These relations are expressed in terms of equations called
equations of motion.
-
Motion: Whenever a body changes its position continuously with respect to
the position of other bodies around it then it is said to be in motion.
Forces
Pushes or Pulls are very general names given to forces. A physicist is much
more precise when describing forces acting on a body using terms like weight,
frictional force, tension, normal reaction force, electrical force, magnetic
force etc.
When a force is applied on a surface in a direction perpendicular to the
surface, the force is called thrust. And the ratio of thrust applied to the
surface area, is the pressure.
The weight of an object is the attractive force exerted by the Earth on it,
due to the gravitational interaction.
Two equal and opposite parallel forces acting along different lines on a body
constitute a couple.
The magnitude that measures the ability of a couple to produce a rotation is
called torque (or angular momentun). The turning effect of the couple is called
its moment and is calculated by the product of either of the forces and the
perpendicular distance between them (i.e., between their lines of action).
An object is said to be stable if it is steady and well balanced so that when
it is pushed slightly it does not topple or fall off easily. Let us try to do a
simple experiment or derive the conditions for stability.
If a body is in equilibrium under the action of a number of forces, then the
algebraic sum of the moments of the forces about any point is equal to zero.
Newton's Laws of Motion
The word force in common usage refers to a push or pull. The word Mass is
also just as familiar as the word force. A super tanker is one that contains an
enormous amount of mass. In comparison a coin does not contain much mass.
-
The word force in common usage refers to a push or pull. The word Mass is
also just as familiar as the word force. A super tanker is one that contains
an enormous amount of mass. In comparison a coin does not contain much mass.
-
Every body continues in its state of rest or of uniform motion in a
straight line unless compelled by some external force to act otherwise.
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Momentum is another vector quantity which has the same direction as that of
velocity. Momentum is a property of the body possessed by virtue of its mass
and velocity. It is the product of mass of the body and its velocity.
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Earlier we have mentioned that application of force can change the velocity
of the moving object. Let us suppose that a body of mass 'm' is moving with a
velocity 'u'. When a force F is applied on the body for 't' seconds, the
velocity changes from the initial velocity 'u' to the final velocity 'v'.
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-
Inertia is the inability of material body to change, by itself, its state
of rest or of uniform motion in a straight line.
Gravitation
We have learnt that a force changes or tends to change the state of rest,
speed or direction of motion of an object, i.e., the force produces an
acceleration. In this chapter, we are going to identify one of the forces which
produces acceleration in all objects on the surface of the Earth irrespective of
their mass.
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We have learnt that a force changes or tends to change the state of rest,
speed or direction of motion of an object, i.e., the force produces an
acceleration. In this chapter, we are going to identify one of the forces
which produces acceleration in all objects on the surface of the Earth
irrespective of their mass.
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What do you observe when you drop a stone from a height? The stone which
was initially at rest starts moving towards the ground and attains a maximum
speed just before it touches the ground.
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Sir Isaac Newton gave a mathematical relation to calculate the force of
gravitation and this relation is known as the universal law of gravitation.
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According to Newton's law of gravitation, the force of attraction is
directly proportional to the mass of the body.
-
Let us now calculate the force of gravitation existing between two unit
masses separated by a unit distance.
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Is Newton's third law of motion applicable to gravitational force? Yes it
is. Let us now see how Newton's third law of motion is applicable to the
gravitational force existing between the various objects in the universe.
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We know that whenever an object is dropped from a height, it falls towards
the Earth. Similarly, when an object is projected vertically upwards, it goes
up but after attaining a certain height, it starts falling down. It is the
force of gravitation which pulls the object towards the Earth. The object,
which is projected vertically upwards, is moving against the force of
gravitation.
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Consider an object of mass m lying on or near the surface of the Earth. Let
Me be the mass of the Earth and Re be its radius i.e., Re
is the distance between the object and the centre of the Earth.
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The motion of a body under gravity is a uniformly accelerated motion and
hence all the equations of motion for uniformly accelerated motion in a
straight line is applicable to the motion of bodies under gravity.
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The Earth's gravitational force causes an acceleration of 5 m/s2 in a 1kg
mass somewhere in space.
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Mass and weight are commonly mistaken as the same, but they are two
different quantities. Now let us try to find out the differences between them.
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We often hear that an astronaut experiences weightlessness in space. What
does this mean? Let us perform a simple experiment to demonstrate
weightlessness.
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So far we have studied only the motion of an object under only one force.
In this section we are going to study the motion of an object acted upon by
two forces acting at right angles to each other. When an object is thrown
horizontally from a certain height from the ground, then the object follows a
curved path. An object thrown into space horizontally under the action of
Earth's gravity is called a "Projectile".
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Place two coins A and B near the edge of a table as shown in the figure.
Simultaneously drop the coin A vertically and flick the coin B horizontally.
After a while we will hear just one clink, showing that both the coins reach
the ground at the same time.
Work, Energy and Power
For a layman the term 'work' implies any activity resulting in muscular or
mental exertion. In physics, however, the term has a different meaning. It
represents a physical quantity.
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For a layman the term 'work' implies any activity resulting in muscular or
mental exertion. In physics, however, the term has a different meaning. It
represents a physical quantity.
-
Let us now discuss the conditions to be satisfied for work to be done. From
the above examples, it is clear that work is said to be done when a force acts
on an object and the point of application of the force moves in the direction
of force.
-
One joule is the work done, when the point of application of a force of one
Newton moves through a distance of one meter in the direction of force.
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Any thing, which is able to do work as defined above, possesses energy. We,
therefore, define energy as the capacity to do work. Energy is measured by the
amount of work that a body can do. Therefore, SI unit of energy is also joule.
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It is a matter of common experience that a fast moving stone can break a
windowpane, falling water can rotate turbines and moving air can rotate
windmills and propel sailboats. In all these examples, the moving body
possesses energy. Work is done by the body in motion. This type of energy
possessed by moving objects, is known as kinetic energy.
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We know that all moving objects possess momentum. Momentum of the body is
defined as the product of its mass and the velocity.
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Water stored in a reservoir is capable of rotating turbines, which are kept
at a lower level i.e, water stored in a reservoir possesses energy.
-
Steam engine- Here the coal burns and the heat due to the combustion of
coal converts water into steam and the expansive force exerted by the steam on
the piston of the engine moves the locomotive.
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Imagine two students positioned at track A and track B of 100m length
shifting 10 bricks from one end of the track to the other end. What is the
amount of work done by each one of them? The amount of work done is same but
the time taken to perform the work varies. In order to find out the fastest
among the two we calculate the work done in unit time. That means work done
and work done in unit are two different quantities.
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All bodies when projected vertically upwards fall back to earth due to the
earth's gravitational pull. The maximum height attained by a body depends upon
the initial velocity of the body.
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The point of application of force must move in the direction of force.
Force Work Power Energy and Machines
From times immemorial, man has used machines to help him in his work. Today,
we are dependent on machine for almost every task. When we think of machines we
always tend to think of big and complicated units with many moving parts like
wheels and rollers and gears and shafts. In Physics the term 'machine' has a
specific meaning.
From times immemorial, man has used machines to help him in his work. Today,
we are dependent on machine for almost every task. When we think of machines we
always tend to think of big and complicated units with many moving parts like
wheels and rollers and gears and shafts. In Physics the term 'machine' has a
specific meaning.
A bicycle is a machine which is used to gain speed. We gain speed by exerting
additional force. When we try to ride a bicycle up a steep hill, we soon realize
that we gain speed by applying greater force. It is impossible to multiply both
the force and gain the speed at the same time.
A simple crowbar can be used to lift a heavy rock with a small effort. The
crowbar is an example of a lever.
In this type of lever the effort and the resistance (load) are situated on
either side of the fulcrum.
In these type of levers the load is situated between fulcrum and effort.
In class III levers effort is situated between the load and the fulcrum.
Pulleys are used in everyday life. They are used in factories for lifting
loads, in hoisting flags, in drawing curtains in theatres, in lifts, in drawing
water from well etc.
A heavy load may be raised more easily by pulling it up along a sloping
surface than by lifting it vertically. For example, heavy barrels are often
loaded into vans by passing two ropes round them and hauling them up an incline
formed by two stout planks held apart by iron rods.
Gears are like a continuously rotating lever. By using different sizes of
wheels, and different numbers of teeth, you can use gears as force multipliers
or as distance multipliers.
At one end of the axle, a wheel of a greater diameter is fixed. The axle and
the wheel both rotate about the same axis. Ropes have been wound around both the
wheel and the axle.
Machine is a device that is used to multiply force, or to gain speed, or to
change the direction of a force, or transform energy.
Static Electric Current
Static electricity was known to people more than 2500 years ago. The Greeks
knew about the attractive property of the resin amber. They knew that by rubbing
amber with cloth, it could be made to attract small feathers. The Greek name for
amber was 'elektron'.
Static electricity was known to people more than 2500 years ago. The Greeks
knew about the attractive property of the resin amber. They knew that by rubbing
amber with cloth, it could be made to attract small feathers. The Greek name for
amber was 'elektron'.
You can electrify a glass rod by rubbing it with silk. Suspend such an
electrified rod by a silk thread as shown in figure. If you bring another glass
rod electrified in the same manner, you will notice that the rods repel each
other.
The existence of negative and positive charges on these materials can be
explained on the basis of the structure of the atom. Almost all the mass of an
atom resides in a central nucleus which contains a number of tightly packed
protons and neutrons.
In case of certain materials like glass, the electrons are firmly 'bound' to
the atoms and they do not normally move. Such materials are known as the
'insulators' or bad conductors of electricity. Polythene, ebonite, silk, fur,
plastic etc. belong to this category. The charge produced by rubbing a glass
does not flow away, because it is an insulator. These charges are called static
because they do not move.
Keeping in mind the structure of the atom, we can easily explain charging by
rubbing. When glass rod is rubbed with silk, some of the electrons from the
atoms on glass are transferred to silk. Because there is a deficiency of
electrons in the glass, it becomes positively charged. On the other hand, as the
silk has acquired additional electrons it becomes negatively charged.
When a charged body is brought near the electroscope the light weight pith
ball is first attracted to the rod. Once it has touched the rod it gets
repelled. When the pith ball comes in contact with the rod some of the charge
from the rod gets transferred to the pith ball. As a result, it acquires similar
charge. Because of the similar charge it then gets repelled. Attraction precedes
repulsion.
It should always be remembered that whenever you have to charge a body, it
must be insulated from the earth. It means that the body should be supported on
a stand which is made of an insulating material which does not allow charges to
pass into the earth.
When the positively charged body is brought near the two cans A and B, the
electrons (-ve charges) from both the cans are attracted and get concentrated on
B which is near R.
To detect a charge on a rod 'A' or 'B' bring the rod near to the metallic
disc or cap of the electroscope. In either case the leaf diverges as shown in
the diagram.
During thunderstorms, large amount of electrical charge separation takes
place in the clouds. As a result, some regions of the cloud have overall
positive charge, while others have overall negative charge.
Then term 'Xerography'; the use of Photoelectric phenomena to transfer an
image from one sheet of paper to another comes from the Greek words for "dry"
and "writing".
One of the greatest discoveries of the eighteenth century was the discovery
of electricity. Think of life today without electricity and you will realize the
part electricity plays in our day to day life.
Your everyday experiences have familiarised you with many electric circuits.
Let us take an example of an electric circuit with a battery (a source of
electricity), toaster and a switch.
Electrons in different metals can have different energies. If two of these
metals are placed in a conducting liquid (electrolyte) a difference in
electrical potential is set up between them. A pair of different metals arranged
in this way is an electrochemical cell. It converts chemical energy to
electrical energy. These cells are known as Primary Cells.
When substances like glass and silk or ebonite and fur are rubbed, positive
and negative charges of equal amount are simultaneously produced.
Magnetism
It is believed that around 2000 BC the Chinese had already discovered the
magnetic property of natural iron ore. In a part of Turkey formerly called
Magnesia, there are deposits of an iron one which has the property of attracting
iron. As this ore was discovered by Greeks they called it magnetite. This
natural magnet was used by mariners for navigation and was called "Lodestone".
It is believed that around 2000 BC the Chinese had already discovered the
magnetic property of natural iron ore. In a part of Turkey formerly called
Magnesia, there are deposits of an iron one which has the property of attracting
iron. As this ore was discovered by Greeks they called it magnetite. This
natural magnet was used by mariners for navigation and was called "Lodestone".
When a bar magnet is suspended freely, it always comes to rest in a
north-south direction. This property is used in the construction of a mariner's
compass.
The magnetic force appears to be concentrated at or near the ends of the
magnet. These areas are called the magnetic poles.
There are two major types of magnets: Permanent magnets and Temporary
magnets. Permanent magnets retain their magnetism over a long period of time
whereas temporary magnets retain their magnetic properties only under certain
conditions like presence of a strong magnet or an electric current in the
vicinity.
To find out about laws of magnetism you can perform the following simple
experiment.
The nail retains its magnetism only as long as the magnet is held near it or
in contact with it. It will even pick up several other nails. But is loses its
magnetism as soon as the magnet is removed. Magnetism produced in this manner
due to the presence of a magnet is called induced magnetism.
Iron gets magnetized faster but loses its magnetism as soon as the inducing
magnet is removed. Hence soft iron is said to have high susceptibility but low
retentivity. This property of soft iron is very useful in making temporary
electromagnets where we need strong but temporary magnets. If the magnets used
in these devices were to retain their magnetism for a longer period, the devices
would not function properly.
Place the soft iron piece AB flat on a table and stroke it with a bar magnet
from A to B with one end of a bar magnet as shown in figure. When the magnet
reaches B it is lifted, and brought back to A to repeat the stroke. After a few
strokes you will notice that A will possess the same polarity as the pole being
rubbed with it.
The best method to demagnetize is by keeping the magnet in a coil through
which an alternating current is passed. When the current starts flowing through
the coil, the magnet is pulled out of the coil in east-west direction and kept
far away. The magnetic field produced due to alternating current changes its
direction continuously. As the magnet is withdrawn far away the magnetization
becomes weaker and weaker until finally the magnet is completely demagnetized.
If two magnets are placed side by side there will be mutual repulsion or
attraction. This weakens the strength of the magnet. To prevent this, bar
magnets are placed side by side with opposite poles near. A soft iron piece
called a keeper is placed across the poles as shown in figure. This soft iron
piece provides a path for the magnetic field lines to form a continuous loop.
Thus it helps in preserving the magnetic field.
A completely satisfactory theory of magnetism has still not been formulated.
At present it is assumed that magnetism is due to the movement of the electrons.
The electrons circulate around the nucleus of the atom.
If a small compass needle is placed at a point near the north pole of a bar
magnet, the needle turns round on its pivot and settles in a fixed direction.
As a result of two magnetic fields acting at the same place, the resultant
field has a special feature. At a particular point, if the compass needle does
not point in any particular direction, then there is no net magnetic field at
the point. Such a point is called Neutral point or the Null point.
About AD1600, William Gilbert, who was a court physician of Queen Elizabeth
of England, performed certain experiments using spherical lodestones. When he
placed small, pivoted magnetic needles at different positions on this sphere, he
found that their behavior was quite similar to that of magnetized needles at
corresponding places on the earth's surface. Later he concluded that the earth
behaves like a huge magnet.
Angle of dip is the angle made with the horizontal by the earth's total
magnetic field.
Heat
Take two beakers one with hot water and another with cold water. Dip your
fingers in hot water your finger experience hotness. Then dip your fingers in
cold water. Your fingers experience coldness.
Take two beakers one with hot water and another with cold water. Dip your
fingers in hot water your finger experience hotness. Then dip your fingers in
cold water. Your fingers experience coldness.
Sun is a natural source of energy. Solar heat energy is essential for the
survival of all forms of life on earth. Solar energy is considered as an
alternate source of energy.
Heat energy is present in every object above absolute zero. How do we know
that heat is present in every object? Temperature of the body is an indication.
Temperature is a physical quantity and hence, measurable. In fact in SI
system, temperature is a fundamental physical quantity.
A reference scale with respect to which the temperatures can be measured is
known as 'scale of temperature'.
Lord Kelvin (1824-1907) devised this scale of temperature. Hence, this is
called the Kelvin scale, and in this scale, temperature is expressed in Kelvin.
In SI system, Kelvin is the unit of temperature.
Matter is made up of atoms and molecules. These atoms in molecules are in a
state of continuous motion. For example, molecules and atoms of a solid can have
only vibrational motion, because they are held in their positions by strong
intermolecular forces.
In CGS system, heat is measured in calories. Calorie is defined as 'the heat
energy required to increase the temperature of 1gm of water through one degree
Celsius'.
When same amount of heat is supplied to different substances of equal mass at
the same initial temperature, rise in temperature for different substances is
different.
The specific heat of a substance is an important physical property because it
tells us the suitability of a given substance for a specific purpose. Aluminium
vessels are used in cooking because aluminium is a light metal. Hence, for a
given volume, its thermal capacity will be less than that of vessels made of
steel of same volume.
Calorimetry is the measurement of the amount of heat evolved or absorbed in a
chemical reaction, change of state, or formation of a solution.
Calculating the molar heat of combustion for quinone with th conditions like
increase in 1 0 C for every 1560 J for a certain material. A 0.1 gram
of quinone (molar mass = 108.1 g/mole) when burnt, resulted in an increase in
temperature from 22 0C to 25.2 0C.
We heat raw food to soften it. We freeze water into ice by cooling it in
refrigerator. When we boil water in a kettle we observe the steam oozing from
the mouth of the kettle.
Matter expands on heating, i.e., solids, liquids and gases expand on heating.
The ratio of increase in length to its original length per every degree rise
in temperature is known as 'the coefficient of linear expansion'.
Expansion in area of a Laminar surface due to heating is known as superficial
expansion.
The coefficient of cubical expansion is defined as the ratio of the increase
in volume to its original volume for every degree increase in temperature. It is
denoted by 'g'.
Liquids do not have a definite shape. They take the shape of the container.
Thus, we can specify a liquid by its volume. Hence, we can speak of volume
expansion only for liquids. Expansion of liquids is much greater than that of
solids.
Gases also expand on heating. Their volume expansion is very much greater
than that of liquids. If a gas is heated at constant pressure, its volume
increases and if a gas is heated at constant volume, its pressure increases due
to expansion. Similarly, if we have to study the variation of pressure with
temperature, its volume must be kept constant.
Heat energy can bring about a change of state in matter from solid to liquid
and liquid to gaseous state.
Take a few pieces of ice in a beaker. Insert a thermometer. Note the
temperature. You will observe it to be 00C.
In liquids, the molecules of the liquid are always in a state of random
motion, within its surface. Some molecules may have sufficient kinetic energy to
escape from the surface of the liquid. This process is known as evaporation.
Evaporation takes place at all temperatures. Rate of evaporation increases with
rise in temperature and becomes maximum at the boiling point of the liquid. The
process of evaporation also increases with increase in surface area of the
liquid.
Humidity is the amount of moisture (water vapor) present in the atmosphere.
This moisture is due to the continuous evaporation of river, lakes, and oceans,
and also from various life activities.
Relative humidity is defined as the ratio of the actual amount of water vapor
in the atmosphere to the absolute humidity at that temperature.
Matter
Today the fact that all matter is made up of atoms is universally accepted.
Realisation of the atomic constituents of matter began in 1828 when Scottish
botanist Robert Brown observed a random ceaseless motion of pollen grains
suspended in a liquid. Many macroscopic properties and phenomena observed can be
explained using this microscopic picture of matter being composed of atoms or
molecules possessing some form of motion.
Today the fact that all matter is made up of atoms is universally accepted.
Realisation of the atomic constituents of matter began in 1828 when Scottish
botanist Robert Brown observed a random ceaseless motion of pollen grains
suspended in a liquid. Many macroscopic properties and phenomena observed can be
explained using this microscopic picture of matter being composed of atoms or
molecules possessing some form of motion.
Matter exists in several phases. If we look at all objects around us, we
perceive that some materials have a definite shape and occupy a definite amount
of space or volume. We call these materials solids and we can name many objects
that are solids. We say that solids have a definite shape and a definite volume.
Brownian motion can be demonstrated simply by releasing some smoke particles
from burning cord into a small glass container and putting a cover plate to seal
the smoke and air into the cell.
If a bottle of perfume is opened in one corner of a room, it spreads in the
whole room by diffusion. If you drop a little ink in a beaker of water it will
spread by itself in the beaker of water and the color spreads uniformly.
The molecules in a solid are very closely packed. The inter-molecular force
of attraction is very strong in solids. Hence solids have a definite size and
shape. Molecules of a solid vibrate about their mean position.
Molecules are in a state of perfect chaos, moving with all possible
velocities in all directions, colliding with each other and with the walls of
the container.
According to modern theory, the molecules of a solid are fixed in relation to
each other. They vibrate in place, but do not wander around. This accounts for
the fact that a solid keeps its own shape. Solids are usually crystalline. A
solid is a crystalline substance in which the molecules, atoms and ions are
believed to be arranged in definite geometrical patters. This geometrical
pattern determines the shape of the crystal.
Materials can be solid, liquid or gaseous, depending upon the arrangement and
freedom of movement of these particles.
Wave Motion and Sound
In the previous chapters we studied the different types of motion like
uniform motion, accelerated motion, projectile motion and periodic motion. We
then learnt to relate the acceleration of the body to the force applied. In this
chapter we shall study the motion of collection of particles - wave motion.
In the previous chapters we studied the different types of motion like
uniform motion, accelerated motion, projectile motion and periodic motion. We
then learnt to relate the acceleration of the body to the force applied. In this
chapter we shall study the motion of collection of particles - wave motion.
A simple pendulum consists of a heavy mass (spherical in shape) suspended by
a long weightless, inextensible and flexible string from a point about which it
can oscillate. The mass which is attached to the end of the string is called the
bob of the pendulum.
A simple pendulum whose time period is two seconds (i.e., on Earth) is called
a Seconds Pendulum. A Seconds Pendulum is used in Pendulum clocks.
weighing with a spring balance or a pan balance is possible due to damping of
the oscillations otherwise it would not have been possible to read the scale.
Most of us have seen the formation of ripples when a pebble is dropped into a
pond. The ripples are produced due to the disturbance created by the pebble. The
ripples travel in concentric circles of ever-increasing radius till they strike
the boundary of the pond.
A mechanical wave is a periodic disturbance, which requires a material medium
(solid, liquid or gas) for its propagation. These waves are also known as
elastic waves because their propagation depends upon the elastic properties of
the medium through which they pass. Examples for mechanical waves are sound
waves and water waves. In these waves, the particles of the medium just vibrate
to and fro about their mean position.
A wave motion in which the particles of the medium oscillate about their mean
positions in the direction of propagation of the wave, is called longitudinal
wave.
Whenever a wave passes through a medium, there is a change in some property
of the medium. Hence, the waves can be graphically represented by showing the
changes in the value of any such property of the medium as the waves travel
through it.
All along when we were discussing about transverse and longitudinal waves the
disturbances, which cause them were continuous. But the disturbances always need
not be continuous i.e., it might last only for a short duration.
Wavelength is defined as the distance between the two nearest points on the
wave or it can be defined as the distance between two consecutive crests or
troughs in the case of a transverse wave or it is the distance between two
consecutive compressions or rarefactions.
Sound is always produced due to the vibration of a body. In some cases the
vibrations of the source may be very small or very large that it may not be
possible to detect them. This type of vibrations is produced by tuning fork,
drum, bell, the string of a guitar etc. Human voice originates from the
vibrations of the vocal chords and the sound from the musical instruments is due
to the vibrations of the air columns. We have already discussed that the sound
travels in the form of longitudinal wave motion. Sound waves require a material
medium for its propagation.
The flash of lightning due to collision of clouds is seen much before the
thunder, although both occur simultaneously. This happens because the velocity
of light is greater than the velocity of sound. The speed of sound depends on
(1) elasticity and (2) density of the medium through which it propagates.
Megaphone: Megaphone is a horn-shaped tube. The sound waves are prevented
from spreading out by successive reflections and are confined to the air in the
tube.
WAVE is a form of disturbance, which travels through a material medium due to
the repeated periodic motion of the particles of the medium about their
position.
Reflection of Light
It is a matter of common experience that the objects inside a dark room,
which are invisible, become visible when the room is illuminated by a source of
light. Thus light can be defined as the external cause responsible for the
sensation of vision.
-
- It is a matter of common experience that the objects inside a dark room,
which are invisible, become visible when the room is illuminated by a source
of light. Thus light can be defined as the external cause responsible for the
sensation of vision.
-
- Light is a form of energy and can be transformed into other forms of
energy. You would have observed the path of 'a beam of light' inside a room.
This beam is nothing but the scattered light produced by the dust particles
and this beam of light becomes invisible if the room is dust free. Thus light
makes things visible even though light by itself is invisible.
-
- Light is a form of energy. Energy can be transferred from one point to
another point either by particle motion or by wave motion. Accordingly,
different theories on the nature of light have been proposed.
-
- Light is a form of energy produced by luminous objects. Light can travel
through vacuum.
-
- In a homogenous transparent medium light travels in a straight line and
this is known as rectilinear propagation of light.
-
- When a ray of light falls on any surface, a part of the light is sent back
to the same medium. This phenomenon where the incident light falling on a
surface is sent back to the same medium is known as reflection.
-
- The figure shows how a ray of light is reflected by a plane surface. Let
MM' represent a reflecting surface. When a ray of light is incident on MM' in
the direction IO it gets reflected along the direction OR. IO is the incident
ray; O is the point of incidence and OR is the reflected ray.
-
- Fix a sheet of white paper on a drawing board. Draw a line MM' on it and
mark a point O at the center of the line and a normal ON on MM'.
-
- An image can be real or virtual. A real image is formed when the rays of
light actually intersect after reflection. A virtual image is formed when the
light rays after reflection do not actually intersect but appear to diverge
from it (these rays of light intersect when produced backwards).
-
- A ray of light incident on a plane mirror at 90o gets reflected
from the mirror along the same path.
-
- It is an instrument in which plane mirrors are used to fold light so that
the image of an object can be brought down to a lower level. It is used for
observing enemy movements from trenches without any danger of being seen.
Sailors on submarines use periscopes to see things above the water level.
-
- A mirror whose polished, reflecting surface is a part of a hollow sphere
of glass or plastic is called a spherical mirror.
-
- To show that f = R/2 where f is the focal length of a mirror and R its
radius of curvature.
-
- All distances are measured from the pole of the mirror. Distances measured
in the direction of the incident ray are positive and the distances measured
in the direction opposite to that of the incident rays are negative.
-
- When an object is placed in front of a concave mirror, light rays from the
object fall on the mirror and get reflected. The reflected rays produce an
image at a point where they intersect or appear to intersect. Formation of an
image by mirrors is usually shown by constructing ray diagrams. To construct a
ray diagram, we need at least two rays whose paths after reflection from the
mirror are known. These rays must be chosen according to our convenience. Any
two of the rays can be considered to obtain the image.
-
- When an object is placed at infinity, the rays coming from it are parallel
to each other. Let us consider two rays, one striking the mirror at its pole
and the other passing through the center of curvature.
-
- The use of a concave mirror depends upon the distance of the object from
the mirror.
-
- Formed between the pole and the focus.
-
- Mirror formula is the relationship between object distance (u), image
distance (v) and focal length.
-
- Let AB be an object placed on the principal axis of a convex mirror of
focal length f. u is the distance between the object and the mirror and v is
the distance between the image and the mirror.
-
- The ratio of the height of the image to the height of the object is called
the linear magnification. It is denoted by the letter m. While deriving the
mirror formula it has been proved that D ACB and D A1CB1
are similar and so also D FB1A1 and D FED are similar.
-
- Light is a form of energy which can be reflected either by a plane or
spherical mirror. Depending upon the type of mirror used for reflection of
light the use of reflecting surface also varies. In the next chapter let us
see what happens when light moves from one medium to another.
Refraction of Light
In the previous chapter we have seen how light gets reflected when it is
incident on a surface. Now let us see what happens when a ray of light traveling
from one medium to another medium of different density.
-
- In the previous chapter we have seen how light gets reflected when it is
incident on a surface. Now let us see what happens when a ray of light
traveling from one medium to another medium of different density.
-
- Let us now see what happens when a ray of light is incident on the
boundary separating the two mediums having different densities. A part of the
light gets reflected and rest of the light changes its direction as it enters
the second medium.
-
- The incident ray, the refracted ray and the normal to the surface at the
point of incidence all lie in one plane.
-
- According to the principle of reversibility of light, the path of a ray of
light is reversible. The figure below shows how light gets refracted from
medium 1 to medium 2.
-
- Place a rectangular glass slab on a white sheet of paper fixed on a
drawing board.
-
- Place a rectangular glass slab on a white sheet of paper fixed on a
drawing board.
-
- Critical angle is that angle of incidence for which a ray of light while
moving from a denser to a rarer medium just grazes over the surface of
separation of the two media (that is, angle of refraction = 90o).
-
- The mirage is caused by the total internal reflection of light at layers
of air of different densities. In a desert, the sand is very hot during day
time and a result the layer of air in contact with it gets heated up and
becomes lighter. The lighter air rises up and the denser air from above comes
down.
-
- A lens is a portion of a transparent refracting medium bounded by two
surfaces which are generally spherical or cylindrical or one curved and one
plane surface.
-
- It is the center of a lens. It is denoted by the letter O. A ray of light
passing through the optical center of a lens does not suffer any deviation. It
is also referred to as optic center.
-
- A ray of light passing through the optical center of the lens travels
straight without suffering any deviation. This holds good only in the case of
a thin lens.
-
- An incident ray of light coming from the object parallel to the principal
axis of a concave lens after refraction appears to come from its focus.
-
- The distances measured in the direction of incident rays are positive and
all the distances measured in the direction opposite to that of the incident
rays are negative.
-
- The relationship between distance of the object (u), distance of the image
(v) and focal length (f) of the lens is called lens formula or lens equation.
-
- Let AB represent an object placed at right angles to the principal axis at
a distance greater than the focal length f of the convex lens. The image A1B1
is formed beyond 2F2 and is real and inverted.
-
- Let AB represent an object placed at right angles to the principal axis at
a distance greater than the focal length f of the convex lens. The image A1B1
is formed between O and F1 on the same side as the object is kept
and the image is erect and virtual.
-
- Magnification is the ratio of the size of the image (hI) to the
size of the object (ho)
-
- Whenever a ray of light passes through a lens (except when it passes
through the optical center) it bends. The bending of light rays towards the
principal axis is called convergence and bending of light rays away from the
principal axis is called divergence.
-
- Our eye is the most important natural optical instrument. The eye is
nearly spherical in shape with a slight bulge in the front part.
-
- The light coming from an object enters the eye through cornea and pupil.
The eye lens converges these light rays to form a real, inverted and
diminished image on the retina.
-
- A normal eye can see both the distant and the nearby objects clearly. In
the case of the eye, the image distance (v) is fixed as the distance between
the eye lens and retina remains the same but the object distance (u) varies.
-
- The range of distance over which the eye can see clearly is called its
range of vision. The range of vision of a normal healthy eye is from infinity
to 25cm from the eye.
-
- A normal eye can see all objects over a wide range of distances i.e., from
25 cm to infinity. But due to certain abnormalities the eye is not able see
objects over such a wide range of distances and such an eye is said to be
defective.
-
- You must have seen middle aged people holding a book away from their eyes
to read properly. This is because they are not able to see the nearby objects
clearly. We say that those people are suffering from hypermetropia (long
sightedness).
-
- You must have seen some people holding books very close to their eyes.
This is because they suffering from myopia (short sightedness). A myopic
person cannot see distant objects clearly because the far point of his eye is
less than infinity.
-
- At times the eye is not able to focus the light coming from the horizontal
and vertical planes. As a result, the horizontal and vertical views of an
object will not be the same. Such a defect of the eye is called astigmatism.
-
- Thus, this chapter on refraction helps us understand many natural
phenomena like the twinkling of stars, the sparkling of diamonds, mirage etc.
It also throws light on the working of the human eye and the defects of
vision.
Dispersion
It is a matter of common experience that precious stones like diamonds,
rubies, etc. or glass pieces glitter when light, particularly white light is
incident on it. In this chapter let us find out why white light incident on a
transparent prism splits into different colours.
-
- It is a matter of common experience that precious stones like diamonds,
rubies, etc. or glass pieces glitter when light, particularly white light is
incident on it. In this chapter let us find out why white light incident on a
transparent prism splits into different colors.
-
- Sir Isaac Newton, while studying the images of heavenly bodies formed by a
lens, found that the image is colored at its edges. In 1665, to investigate
this, he performed an experiment using a prism.
-
- Even though all colors of the visible spectrum travel with the same speed
in vacuum, the speed of the colors of the visible spectrum varies when they
pass through a transparent medium like glass and water. That is, the
refractive index of glass is different for different colors.
-
- Recombination of the seven colors of the dispersed white light to get
white light is known as Recomposition of white light.
-
- Color may be defined as the visual sensation which depends upon the
wavelength or frequency of the light that enters the eye.
-
- A pair of colors which on mixing produce white are called complementary
colors.
-
- The color of a non-luminous, opaque object depends upon the color of the
light reflected by it. The color of the reflected light depends upon the color
of the incident light.
-
- Any object which allows light to pass through it is known as a transparent
object. The color of any transparent object is the color of the light
transmitted by it.
-
- The retina of our eye is composed of light sensitive cells. Light
sensitive cells are of two types namely, rods and cones. There are three types
of cones., those that are stimulated by low frequencies, those stimulated by
intermediate frequencies and those stimulated by higher frequency visible
light.
-
- Color deficiency is that defect of the eye due to which a person is not
able to distinguish between certain colors mainly due to the malfunctioning or
absence of a particular cone.
-
- The structure and the number of rod shaped and cone shaped cells are
different for animals and birds. For e.g., bees have cones sensitive to
ultraviolet rays.
-
- Is the visual sensation which depends upon the wavelength or frequency of
light that enters the eye.
Optical Instruments
The previous chapter dealt with the refraction of light by lenses and also
about the formation of various types of images by a lens for different positions
of the object. In this chapter let us find out how lenses are used in optical
instruments like microscopes and telescopes to obtain magnified image of an
object.
-
- The previous chapter dealt with the refraction of light by lenses and also
about the formation of various types of images by a lens for different
positions of the object. In this chapter let us find out how lenses are used
in optical instruments like microscopes and telescopes to obtain magnified
image of an object.
-
- A microscope is an optical device which produces a highly magnified image
of very small object such as micro-organisms. Based on the design, there are
two types of microscopes. They are, simple microscope and compound
microscopes.
-
- A simple microscope is nothing but a single biconvex lens. It is referred
to as magnifying glass.
-
- A compound microscope is an optical instrument which is used to magnify
very small objects like blood cells, bacteria which otherwise cannot be seen
with the naked eye.
-
- Telescope is an optical instrument which is used for viewing heavenly
bodies and distant objects.
-
- This type of telescope is used to view heavenly bodies like stars, planets
and satellites.
-
- Microscope is an optical device which produces a highly magnified image of
a very small object.
Electricity, its Heating, Chemical and Magnetic Effects
Appliances used in our day to day life are based on the principles of
electricity and magnetism. Electricity is one of the most important sources of
energy. Lights, fans, motors, radios and television are some common appliances
which work on electricity.
-
- Appliances used in our day to day life are based on the principles of
electricity and magnetism. Electricity is one of the most important sources of
energy. Lights, fans, motors, radios and television are some common appliances
which work on electricity.
-
- 'Electrical potential' is a condition, which determines the direction of
the flow of charge.
-
- The electrostatic potential is defined as the work done in bringing a
single positive charge from infinity to a point (Any point outside the
electric field or space is called infinite point). The unit of potential is
volt (symbol V).
-
- If two charged bodies of different potential are placed one beside the
other, the charges will not move from one body to the other. But if the two
bodies are connected using a conductor, the flow of charges takes place.
Charges will flow as long as there is potential difference between the two
bodies. This rate of flow of electric charge is called 'electric current'.
-
- Batteries produce electricity by converting chemical energy into
electrical energy. Batteries provide electricity to torches, transistors,
toys, clocks and watches.
-
- The devices which deliver electricity are called the 'sources'. Lamps,
electric engines, etc. which consume electricity are called ‘loads’. Switches
are used to switch the loads on and off whenever necessary. Hence, the source,
the loads, and the switches are connected to form electrical circuits.
-
- In the year 1820 a French physicist, Andre Ampere made many discoveries on
the nature of electricity. While a German physicist, Georg Ohm showed that the
flow of an electric current through a wire depended on its 'resistance' and
the potential difference between its ends.
-
- Substances which do not allow electricity to pass through them easily are
called insulators. These are made from materials which have a high resistance.
Some substances which are insulators are air, plastic, cotton, rubber, wood,
paper, glass, pure water, etc.
-
- Resistors can be combined in different ways. When two or more resistors
are connected end to end, so that the same current flows through all of them
then, the resistors are said to be in series.
-
- Let us consider two resistances 'R1' and 'R2'
connected in series. A battery of 'V' volts is applied to the ends of this
series combination.
-
- Connect two resistors 'R1' and 'R2' in parallel to
one another between the points A and B. Connect this combination to a battery
of potential 'V'.
-
- Energy exists in various forms such as mechanical energy, heat energy,
chemical energy, electrical energy, light energy and nuclear energy. According
to the law of conservation of energy, energy can be transformed from one form
to another.
-
- The power is the rate of doing work or in other words, it is the work done
in one second.
-
- Kilowatt - hour is the commercial unit of electrical energy. We have seen
that power is the rate of energy consumed or delivered. If 1 joule of energy
is used per second, we say that energy is used at the rate of 1 watt.
-
- Generally electrical appliances such as an electric bulb, geyser, heater,
etc. are rated with power and voltage. If a bulb is rated 100W - 250V, it
means that when a bulb is lit on a 250V supply, it consumes 100 W of electric
power. This means that, 100 J of electrical energy gets converted into heat
and light energy in 1 second.
-
- The fact that chemical changes produce electrical effect was discovered
accidentally in 1971, by Luigi Galvani, an Italian professor. He found that an
electric current flowed across two dissimilar metals. Volta, professor of
natural philosophy successfully reproduced some of Galvani's results using
inanimate things. The basic reason for electrochemical effects became clear
rather slowly. Scientific investigations in this field actually began with the
converse phenomenon namely chemical effects of electrical currents.
-
- Major progress in understanding magnetism came after the relationship
between electricity and magnetism was established by Hans Christian Oersted in
1820. He found that an electric current moves a compass needle and this effect
lasts as long as the current flows through the wire. It is then possible to
produce magnetism without any magnetic substance at all.
-
- An electric motor is a device which converts electrical energy into
mechanical energy.
-
- The electric generator is a machine for producing electric current. The
electric generator or dynamo converts mechanical energy into electrical
energy.
-
- If the current flows always in the same direction, it is called 'direct
current'. Direction current is represented as DC or dc. The current derived
from a cell or a battery is direct current - since it is unidirectional. The
positive and negative terminals are fixed. If the current changes direction
after equal intervals of time, it is called alternating current. Alternating
current can be written as AC or ac. Most of the power stations generate
alternating current. The following are the circuit elements representing dc
and ac.
-
- Electric power is usually generated at places which are far from the
places where it is consumed.
-
- An electric fuse is a device which is used to limit the current in an
electric circuit. The use of a fuse is to safeguard the circuit and the
appliances connected in the circuit from being damaged.
-
- Usually an electric appliance such as a heater, an iron, etc. are fitted
with all the 3 wires namely live, neutral and earth. The earth wire is
connected to the metallic body of the appliance. This is done to avoid
accidental shock. Suppose due to some defect, the insulation of the live wire
inside an electric iron is burnt then the live wire may touch the metallic
body of the iron.
-
- Electric potential is the condition that determines the flow of charge.
Electrical potential at a point in an electric field is defined as the amount
of work done in bringing a unit of positive charge from infinity to that
point.
Sources of Energy and Nuclear Fission and Fusion
Man is surrounded by an ocean of energy. Mankind has tapped only a fraction
of it. The most colossal dynamo of all is the sun, an unimaginable vast
powerhouse which affects everything on earth. From time immemorial man has
learnt to harness this energy. In 100 B.C. Romans used coal as a fuel to produce
fire. In 650 B.C. windmills were used to help travel from place to place. Steam
engines later replaced horses and developed into locomotives as modern means of
transport.
-
- Man is surrounded by an ocean of energy. Mankind has tapped only a
fraction of it. The most colossal dynamo of all is the sun, an unimaginable
vast powerhouse which affects everything on earth. From time immemorial man
has learnt to harness this energy. In 100 B.C. Romans used coal as a fuel to
produce fire. In 650 B.C. windmills were used to help travel from place to
place. Steam engines later replaced horses and developed into locomotives as
modern means of transport.
-
- The supply of energy to the mankind in the present day world is from many
different sources.
-
- Sunlight falling on the earth's surface equals 50,000 times the energy
used each year by man. Almost all our energy comes from sun.
-
- A solar heating device is one which allows collection of a large amount of
heat from the sunlight in a given region and restrict the loss of heat to the
surrounding in the form of radiation.
-
- Here heat is absorbed by a blackened metallic pipe or plate and water
circulated through these pipes gain heat.
-
- Solar cells are expensive and are used only when supplying electricity
becomes difficult.
-
- It does not cause any environmental pollution like the fossil fuels and
nuclear power.
-
- Wind energy is one of the first sources of energy known to man.
-
- A device in which wind is used to rotate the blades of a fan like
structure is called a windmill. The windmill works on a very simple principle.
When the blowing wind strikes across the blades of a windmill it exerts a
force which rotates its blades.
-
- The picture shows a seven storey-high 17m wind turbine producing 60 KW of
power from a wind with a velocity of 45 km/h.
-
- Water, being a vital resource for all living beings, is also an important
source of energy. Hydropower supplies 6% of the world's energy needs. Moving
water is highly energized. A hand held into a fast flowing stream can feel the
pressure of water trying to push the hand along.
-
- The tides are formed due to the gravitational force of attraction between
the earth, sun and moon. During high tides sea water is trapped in a
reservoir, and released later to drive turbines, which in turn produces
electricity. The block diagram given below illustrates the transformation of
energy.
-
- The electricity produced from flowing water is called Hydroelectric power.
The world's first hydroelectric power plant was set up in 1882 in Wisconsin
USA. It had a very small output, supplying power only for about 250 light
bulbs. But from this small start the production of hydroelectricity has grown
steadily, and today 6% of the world's need is met with hydroelectricity.
-
- The demand for electricity varies at different times of a year. One big
disadvantage is that the wind, waves and tides do not occur at all time and
hence cannot guarantee steady production of electricity. Hydroelectric power
stations can solve this problem. When the demand is low, excess power
generated from other stations can be used to pump water back up into the high
reservoir.
-
- Ever since the earth was formed, huge amount of heat energy has been
stored in its molten core. Some of this heat is always flowing towards the
surface. This heat is called Geothermal Energy.
-
- The first cavemen took firewood from the forests as fuel. Even today
firewood is still the main source of fuel for cooking in many parts of the
world.
-
- Animal dung in the form of dried cakes is also burned for domestic
purposes. Animal dung contains vital nutrients. If burnt directly they produce
a lot of smoke leading to air pollution. Instead animal dung can be converted
into biogas which is a clean fuel. The residue which is rich in nutrients can
then be used as manure.
-
- Biogas is a clean and efficient fuel. It is a mixture of methane (CH4),
carbon dioxide (CO2), hydrogen (H2) and hydrogen
sulphide (H2S).
-
- Water hyacinth, (weeds that clog major waterways) restricting boat traffic
are held in check in a lagoon by careful harvesting. Biogas plants use these
dried plants as raw materials.
-
- The Earth contains many resources which are not being replaced. These
resources which are not being replaced are called non-renewable sources.
Amongst the most non-renewable resources are the three fossil fuels - coal,
petroleum and natural gas.
-
- Coal varies in quality according to the amount of pressure and heat to
which it is subjected to during its formation. Coal consists largely of
carbon, hydrogen and oxygen and a small amount of sulphur. It comes in 3
forms.
-
- When coal is heated without air, it does not burn but produces many
by-products. This process of heating coal in the absence of air is called
destructive distillation of coal.
-
- Petroleum is a dark, viscous, foul smelling liquid, a mixture of solid,
liquid and gaseous hydrocarbons with traces of salt, rock particles and water.
-
- Separation of petroleum into simpler fractions after the removal of
unwanted materials.
-
- The burning of a substance is called combustion. It is an exothermic
process (chemical reactions which give out heat to the surroundings are called
exothermic reactions).
-
- Nuclear energy is the energy released when certain changes take place in
the nucleus of an atom. Nuclear energy is partly renewable and partly
non-renewable source of energy.
-
- The process of splitting of a nucleus of a heavy atom into a number of
light nuclei with the liberation of large amount of energy and two or three
neutrons is called nuclear fission.
-
- The sun is the most enormous and direct, source of energy. Where does this
enormous energy that the sun radiates come from? The source of this energy was
not known to mankind until the year 1939. It was a German physicist, Hans
Bethe, who proposed that the sun contains hydrogen nuclei in its core, moving
at large speeds. Whenever these nuclei fuse to form a nucleus of a heavier
element, a large amount of energy is liberated. Such a reaction is known a
nuclear fusion reaction.
-
- Nuclear reactor is a furnace or an equipment in which the nuclear chain
reaction is carried out in a controlled manner and the heat energy so
liberated is converted into electricity.
-
- In order to live and enable ourselves to do everyday work we need energy.
The prosperity of a country depends upon the availability of energy. Huge
amount of electrical energy is used to run the air conditioners, cold storage
and other domestic appliances. A large share of energy is needed for
transportation. There has been increase in the world's population year after
year.
-
- Today most of our energy needs are supplied by the fossil fuels. In one
hundred years coal will be the only one left as petroleum products may remain
only for 3 to 4 decades. Little of stored energy will be left if we continue
to use energy at the same rate.
The Universe
It was once believed that the earth was the center of the universe and that
everything moved around it. It was later discovered that the earth moves around
the sun.
-
- It was once believed that the earth was the center of the universe and
that everything moved around it. It was later discovered that the earth moves
around the sun.
-
- The solar system consists of the sun and all the objects that travel
around it. The solar system includes the earth and eight other planets, along
with the satellites (moons) that travel around most of them; planet like
objects called asteroids; chunks of iron and stone called meteoroids; bodies
of dust and frozen gases called comets and drifting particles called
interplanetary dust and electrically charged gas called plasma that together
make up the interplanetary medium.
-
- The sun is at the center of the solar system. Its mass is about 740 times
as great as that of all the planets combined. The huge mass of the sun creates
the gravitation that keeps the other objects traveling around the sun in an
orderly manner.
-
- Planets are the largest objects in the solar system except for the sun.
Unlike the sun, the planets do not produce their own energy. They reflect the
heat and visible light produced by the sun. The four planets near the Sun -
Mercury, Venus, Earth and Mars are called terrestrial (earth-like) planets
because they are somewhat similar in size and composition to the earth. They
appear to consist chiefly of iron and rock. The terrestrial planets and Pluto
are the smallest planets. The earth has one satellite, Mars has two, and Pluto
has one. Mercury and Venus have no satellites.
-
- Asteroids are very small planets of rock and metal, which revolve round
the sun mainly between the orbits of Mars and Jupiter. This area is known as
the asteroid belt. Most of the asteroids have a diameter of only 1 kilometer.
But some of them have diameters of more than 100 kilometers.
-
- A satellite is a solid heavenly body that revolves round a planet. The
moon revolves round the earth, so moon is a satellite of the earth. The inner
planets have few moons. Earth has one, and Mars has two tiny satellites.
-
- Many scientists believe that our solar system was formed from a giant,
rotating cloud of gas and dust known as the solar nebula. According to this
theory, the solar nebula began to collapse because of its own gravity. Some
astronomers speculate that a nearby supernova (exploding star) triggered the
collapse. As the nebula contracted, it spun faster and flattened into a disk.
-
- Exploration of the planets by space probes has expanded our understanding
of the solar system. Modern theories about the earth's origin explore how the
earth fits into the solar system, the Milky Way galaxy, and the universe as a
whole. Most scientists agree that the earth was probably formed at the same
time as the rest of the solar system.
-
- In outward appearance, the earth is a nearly spherical ball with a radius
of 6350 kilometers. Internally, the earth consists of three major layers.
-
- A star is a dense cloud of hydrogen and helium gas contracting under its
own gravitational pull. In all the stars hydrogen atoms are continuously
converted into helium atoms and this process is accompanied by a large amount
of energy. This energy is radiated in the form of heat and light.
-
- The life cycle of a star begins with the accretion of hydrogen and helium
gas at -173oC into smaller dense clouds, which contract under their
own gravity. This dense cloud of gas contracting under its own gravity is
called a Protostar. A cloud of gas from which a star is born is known as
Nebula.
-
- Constellation is a group of stars visible within a particular region of
the night sky. The stars that appear in the form of closed groups and form
recognizable shapes and patterns are known as constellations. There are about
88 different constellations across the whole sky. But no one can see them all.
This is because people in the northern part of the world see different stars
from people living in the south. There are far more bright stars in the
southern skies than in the north.
-
- The sun and all the stars that we see are part of our Galaxy. A galaxy is
a congregation of millions or billions of stars held together by gravity.
Apart from the stars, a galaxy also contains dust and hydrogen gas. Galaxies
are the building blocks of this universe. There are millions of galaxies
besides ours in the universe. Some are huge while other, are dwarf galaxies.
-
- Universe consists of all matter and all light and other forms of radiation
and energy. It consists of everything that exists anywhere in space and time.
-
- The solar system consists of sun, the nine planets and their satellites
and thousands of other smaller heavenly bodies such as asteroids, comets and
meteors.
Space Exploration
In the second century AD a Greek writer named Lucian wrote a story about a
trip to the moon. He did not even know how far the moon was but his story
revealed that the idea of space travel was certainly not new.
-
- In the second century AD a Greek writer named Lucian wrote a story about a
trip to the moon. He did not even know how far the moon was but his story
revealed that the idea of space travel was certainly not new.
-
- To place a satellite into orbit it needs to be accelerated in several
stages. The required acceleration is produced by firing rockets at various
stages of flight. These rockets are fitted into a system called 'launch
vehicle' which carries the satellite.
-
- As soon as rockets could break away from the earth's gravity, moon became
the next goal. Russians took the lead landing their spacecraft LUNA-3 which
photographed the far side of moon in 1959. Meanwhile, the United States
launched 11 unmanned moon missions without a single one completing its
objective. Then the Apollo programme began and on July 21, 1969, Apollo-11
landed the first astronauts on the moon.
-
- Expertise is required in the planning, designing and fabrication of
satellites. Each satellite has to be designed according to the purpose for
which it is used. Also, one should have the basic infrastructure to fabricate
the parts of the satellite with high degree of precision and to assemble the
satellite.
-
- Low earth orbit lies in the equatorial plane just lying above the
atmosphere a few hundred miles up.
-
- Communication satellites are normally geostationary satellites. They have
devices called transponder which receive signals from an earth station and
transmit them in different directions. The signals in the form of
electromagnetic radiation are transmitted from the earth station and these
signals are received by the satellite.
-
- Scientists who investigate weather phenomenon are called meteorologists.
To study a particular feature, may require an observation from a larger area.
By combining great number of observations and analysing them by computers it
is possible to get information about a large weather system.
-
- The cameras used on Landsat satellites are extremely complex. They use a
process called remote sensing, in which the cameras scan the earth to look for
different patterns of radiation.
-
- Unfolding the mysteries of the dark and silent space with no known
boundaries has always been a dream of the human race. The desires of man has
ultimately been accomplished through the exploration of space using various
space launching vehicles, space probes and satellites.
Modern Physics
You have learnt in the earlier chapters that flow of electrons constitutes an
electric current and current can be generated from a battery or a generator.
Scientists later discovered that there are many other ways of producing the
stream of electrons.
-
- You have learnt in the earlier chapters that flow of electrons constitutes
an electric current and current can be generated from a battery or a
generator. Scientists later discovered that there are many other ways of
producing the stream of electrons.
-
- The emission of particles from a hot filament was first discovered by
Thomas Edison in 1883 but the effect was left unexplained until the discovery
of the electron by J.J. Thomson in 1897.
-
- When the pressure in the discharge tube is less than 10-4 mm of
Hg, the discharge tube starts showing fluorescence. When this fluorescence was
investigated, it was found that the fluorescence consisted of beams of
negatively charged electrons. These electrons emanate normally from the
cathode. As these emanate from the cathode, the rays are called the Cathode
Rays.
-
- The discovery of the phenomenon of radioactivity was purely accidental. In
1896, Henry Becquerel, a French scientist accidentally found that in presence
of salt of uranium, photographic plates got heavily fogged even though they
were wrapped in opaque paper. He concluded that the uranium salt must be
giving off penetrating radiations similar to X-rays discovered one year
earlier. Two years later, Madam Curie named the phenomenon radioactivity.
-
- It is independent of external factors such as pressure, temperature, state
of substance, electrical field, magnetic field, catalyst etc.
-
- A radioactive nucleus or element emits an alpha or a beta particle and
gets converted into a new nucleus or element.
-
- A nuclide is any species of atom of which each atom has an identical
proton number and also an identical nucleon number. Different nuclides, which
have the same proton number (but different nucleon numbers) are called
isotopes (isotopic nuclides).
-
- In astronomy, the low temperature microwave radiation that arrives at the
earth's surface from all directions of outer space is called background
radiation. It is so named because it forms a background to all the radio
sources that have been detected by radio telescopes.
-
- Surprisingly, the mass of the nucleus is less than the sum of the masses
of the individual protons and neutrons which makeup the nucleus. The lost mass
(mass defect) has been changed into the energy necessary to bind the nucleus
together.
-
- A nuclear reactor is a device for obtaining and using the energy from a
controlled nuclear chain reaction. Controlled means the rate or speed of the
nuclear fissions can be changed by the operator. Most reactors are constructed
in a similar manner. The six main parts of a nuclear reactor are fuel,
moderator, control rods, coolant, heat exchanger, and safety shields.
-
- The first and only atomic bombs were used in war was in 1945 when
Hiroshima and Nagasaki were devastated. Widespread destruction and damage were
produced immediately by the blast.
-
- Waste products from nuclear power stations etc. are becoming a serious
problem. They should be put where the radiation can do no harm. Unfortunately,
there is no way of stopping a radioactive nucleus from emitting radiation.
-
- Nuclear energy is released when very small particles of matter split or
combine. After the split or combination, they result in small particles or
heavy particle. The rest of the mass is changed into energy. This process of
changing mass into energy produces the energy.
-
- When certain metals are heated to a high temperature, they emit thermions
(electrons) and the phenomenon is called thermionic emission
Kinematics
Mechanics, the oldest physical science, is the study of motion of objects. It
is applied in calculation of the path of an artillery shell, a space probe sent
from earth to Mars, etc.
-
- Mechanics, the oldest physical science, is the study of motion of objects.
It is applied in calculation of the path of an artillery shell, a space probe
sent from earth to Mars, etc.
-
- A real object can rotate as it moves. For example, a cricket ball may be
spinning while it is moving, as a whole, in a trajectory.
-
- Rest and motion are relative terms. A person sitting in a moving car is at
rest with respect to his or her fellow passengers, but is in motion with
respect to other objects or people on the road. Moreover, it is not possible
to define 'absolute rest' or 'absolute motion'. Absolute rest is the complete
absence of motion which is not possible to visualise because all the objects
in this universe - electrons in an atom, molecules in solids or gases, solar
systems in galaxies etc., are in motion.
-
- A body is said to be in motion if its position changes with respect to its
surrounding. In order to completely describe the motion of such objects, we
need to specify its position.
-
- During motion in a straight line, the point object occupies a definite
position on the path at each instant. Therefore, to describe the motion, one
should specify the length of the path covered by the point object and the
instant of time.
-
- An object is said to be in non-uniform motion if it undergoes equal
displacement in unequal intervals of time, however small these intervals may
be.
-
- The rate of change of position of a particle in a particular direction
gives the velocity of the particle. It may also be defined as the time rate of
change of displacement of a particle. Velocity is a vector quantity.
-
- Most of the motion that we come across in daily life is non-uniform
motion. Moving objects are either 'speeding up' or 'slowing down'. In
non-uniform motion, the velocity of the moving object changes, as a result of
which the object is said to have an acceleration.
-
- The acceleration of a moving point is the rate of change of its velocity.
Note that the acceleration of a moving object is a vector, as it has both
magnitude and direction.
-
- The velocity-time graph passes through the origin and is inclined to the
time-axis such that the angle of inclination is greater than 0o and
less than 90o.
-
- The velocity-time graph for uniformly accelerated rectilinear motion
(motion along a straight line).
-
- In this section, Let us understand how the position changes with time when
the velocity changes uniformly with time.
-
- The velocity-time graph for uniformly accelerated motion of a particle is
illustrated in the figure. Any two points A, B are chosen on the velocity-time
graph from which perpendiculars AC, BD, AE, BF are dropped on the time and
velocity axes respectively. The coordinates of the points A and B are [t,
v(t)] and [tl, v(tl)] respectively.
-
- The velocity-time relationship which has been derived graphically earlier,
can also be obtained with the help of calculus.
-
- Integrating the above equation and applying the limits which are at s = 0,
initial velocity = u after a distance s has been covered, the final velocity =
v.
-
- A change of position of a particle is called displacement. If a particle
moves from a position A to a position B.
-
- Collinear vectors are those vectors that act either along the same line or
along parallel lines. These vectors may act either in the same direction or in
opposite directions.
-
- It is a vector having unit magnitude. It is used to denote the direction
of a given vector.
-
- Fixed vector is that vector whose initial point or tail is fixed. It is
also known as localised vector.
-
- Displacement vector is a vector which gives the position of a point with
reference to a point other than the origin of the coordinate system.
-
- The multiplication of a vector by a real number assumes a lot of
significance in such statements as - velocity of car B is double the velocity
of car Al.
-
- Two vectors are said to be equal if they have the same magnitude and
direction.
-
- Zero vector or null vector is a vector which has zero magnitude and an
arbitrary direction.
-
- The above example can be stated in the following way as the law of
parallelogram of vectors - If two vectors, acting simultaneously at a point,
can be represented both in magnitude and direction by the two adjacent sides
of a parallelogram drawn from a point, then the resultant is represented
completely, both in magnitude and direction by the diagonal of the
parallelogram passing through the point.
-
- If a number of vectors are represented by the sides of a closed polygon
taken in order, then, their resultant is zero.
-
- The process of splitting a vector is called resolution of a vector. In
simpler language it would mean, determining the effect of a vector in a
particular direction. This is explained with the help of an example later on.
The parts of the vector obtained after splitting the vector are known as the
components of the vector.
-
- It was mentioned earlier that, displacement vectors are added to
displacement vectors, or velocity vectors are added to velocity vectors. Just
as it is meaningless to add scalar quantities of different kinds, such as mass
and temperature, so also it is meaningless to add vector quantities of
different kinds, such as displacement and electric field strength.
-
- When both the cars are moving in the same direction, i.e., q = 00 degrees.
-
- Imagine rotating a right handed screw whose axis is perpendicular to the
plane formed by a and b so as to twist it from a to b through the angle p
between them.
-
- In this chapter, we will consider motion in two dimensions taken to be the
X-Y plane, for convenience.
-
- A particle is said to move with uniform velocity if it undergoes equal
displacements in equal intervals of time, however small these intervals may
be.
-
- A particle is said to move with uniform acceleration if its velocity
changes by equal amounts in equal intervals of time, however small these
intervals may be.
-
- The curved line in the figure represents the trajectory of a particle. Let
the particle be at P at time t.
-
- Projectile motion is an example of curved motion with constant
acceleration. This is the two dimensional motion of a particle thrown
obliquely into the air. The ideal motion of a cricket ball, a golf ball or a
bullet is an example of projectile motion. We assume that the effect air could
have on their motion is negligible.
-
- v Cosq along X-axis which is constant, since, the
force of gravity in the horizontal direction is zero.
-
- Maximum height is denoted by the letter hmax or H. It is also
known as the vertical range. It is the maximum height to which a projectile
rises above the horizontal plane of projection.
-
- The revolution of moon around the Earth and the revolution of an
artificial satellite in a circular orbit round the Earth are examples of
circular motion.
-
- Definitions of displacement, uniform velocity, variable velocity, average
velocity, speed and instantaneous velocity with examples.
Laws of Motion
Whenever we push or pull an object, we do so by means of a force. Force is an
interaction between two bodies which causes acceleration, or simply, motion.
-
- Whenever we push or pull an object, we do so by means of a force. Force is
an interaction between two bodies which causes acceleration, or simply,
motion.
-
- An interaction which causes an acceleration is called a force. Only when
we push a ball does it begin to move. A ball lying on a horizontal floor
doesn't start to move all by itself. For that matter, take a parked a car on a
horizontal road. Only when we activate the engine and engage the gears does
the engine impose some force on the wheels, which in turn, imposes force on
the road to begin motion.
-
- Every body continues in its state of rest or of uniform motion in a
straight line until and unless acted upon by an external force.
-
- The rate of change of momentum of a body is proportional to the applied
force and takes place in the direction in which the force is applied.
-
- Springs are simple devices that are commonly used. It is used in shock
absorbers in automobiles, in push-back ballpoint pens, in electrical measuring
instruments, etc. The spring possesses a simple property by the virtue of
which, when compressed or elongated, it tries to attain its original state.
-
- The effect of a force not only depends on its magnitude but also on the
time for which the force acts. When a large force acts for a very short time,
one more important parameter comes into play.
-
- Newton's third law states that to every action, there is always an equal
(in magnitude) and opposite (in direction) reaction.
-
- The law of conservation of momentum states that the total vector sum of
momenta of bodies, in an isolated system, along any straight line remains
conserved and remains unchanged due to reaction forces between the forces of
the system.
-
- If three concurrent forces acting on a body keep it in equilibrium, then
each force is proportional to the sine of angle between the other two forces.
-
-
- Circular motion is commonly seen in both microscopic and large systems.
Motion of the electron, planetary motion and rotation of tyres are common
examples of circular motion. What is circular motion? It is a type of motion
exhibited by a particle or set of particles moving around a fixed point at a
constant distance from that point.
-
- Suppose a particle P is moving in a circle as shown below. Let O be the
centre and OX be the X-axis. The position of the particle may be described by
the angle q.
-
- Consider a particle moving in a circle or radius r with a constant speed
v.
-
- Some examples of horizontal circular motion are planetary motion (which
may or may not be circular), merry-go-round and motion of electrons around the
nucleus.
-
- Consider a body of mass 'm' tied to a string and rotated in a vertical
circle of radius 'r'. The velocity (speed) of the body keeps changing. It is
maximum at the bottom and a minimum at the top.
-
- When vehicles go through turnings, they travel along a nearly circular
arc. There must be some force which will produce the required acceleration. If
the vehicles go in a horizontal circular path, this resultant force is also
horizontal. Consider the situation in which a car of weight mg is moving on a
horizontal circular road of radius r with a constant velocity v.
-
- Friction is not always reliable at circular turns if high speeds and sharp
turns are involved. To avoid dependence on friction, the roads are banked at
the turn so that the outer part of the road is somewhat lifted up as compared
to the inner part.
-
- In order to take a safe turn, the cyclist has to bend a little from his
vertical position. In this case, a component of the reaction provides the
required centripetal force.
Work, Energy and Power
Newton's laws of motion help us to analyse many kinds of motion. But the
analysis is complicated, requiring details about the motion that we simply do
not know.
-
- Newton's laws of motion help us to analyse many kinds of motion. But the
analysis is complicated, requiring details about the motion that we simply do
not know.
-
- Let us consider a situation where the force is acting along the X-axis and
the magnitude of the force is varying with position 'x'. Thus, as the ball
moves, the magnitude of the work done by the force, on the ball, changes. The
adjacent graph shows the plot of a one dimensional variable force.
-
- Energy is a number that we associate with a system of one or more objects.
If a force acts on one of the objects, making it move, then the number
changes. After countless experiments, scientists and engineers realised that
if the scheme by which we assign these energy numbers is planned carefully,
then the numbers can be used to predict the outcome of experiments. However,
learning how to use the numbering scheme is not easy. Let us focus on one form
of energy - kinetic energy.
-
- A contractor wishes to lift a load of bricks from the sidewalk to the top
of a building by means of a winch. Since we know the expression for work, we
can calculate work to be done by the force applied by the winch to lift the
load. We are interested in the rate at which it is done, that is, will the job
take 5 minutes or a week.
-
- According to this principle, work done by a force in displacing a body,
gives the measure of the change in kinetic energy of the body.
-
- As we go higher above the surface of the Earth, the value of acceleration
due to gravity decreases. But for those heights which are very small when
compared to the radius of the Earth, g (and hence mg) can be assumed to be
constant.
-
- Consider a massless spring of natural length 'l', one end of which is
fastened to a wall. The other end is attached to a block, which is slowly
pulled on a smooth horizontal surface, to extend the spring.
-
- If the work done by a force depends only on the initial and final states
and not on the path taken, then it is a conservative force.
-
- We can see many situations in which energy is transferred to or from
objects and systems, similar to money being transferred between accounts. In
each situation, we assume that the energy that was involved can be accounted
for, that is, energy cannot appear or disappear. Energy obeys the law of
conservation of energy, which is concerned with the total energy of the
system.
-
- Conversion of gravitational potential energy to kinetic energy: When a
body falls from a certain height, its kinetic energy increases.
-
- A Karate expert strikes a board of mass 0.14 kg and breaks it, with his
fist of mass 0.70 kg. He then does the same to a 3.2 kg concrete block.
-
- It is that elastic collision in which the colliding bodies move along the
same straight line before and after the collision.
-
- If the colliding bodies do not move along the same straight line path,
then the collision is said to be an oblique collision.
-
- Energy can manifest itself in a number of forms. We have already seen that
it can be in the form of mechanical energy, which is subdivided into kinetic
energy and potential energy.
-
- According to Newton's second law of motion, F = ma.
-
- According to Newton's second law of motion, force acting on a body is
defined as the rate of change of its momentum.
-
- In physics, the concept of energy plays the role of the money. Work is
transferred to or from an object by means of force acting on the body. Energy
transferred to the body is positive work and the energy transferred from the
body is negative work.
Motion of System of Particles and Rigid Body
Physicists love to look at something complicated and find in it, something
simple and familiar. Here is an example. If you flip a baseball bat into the
air, its motion as it turns, is clearly more complicated than that of a
non-spinning tossed ball, which moves like a particle.
-
- Physicists love to look at something complicated and find in it, something
simple and familiar. Here is an example. If you flip a baseball bat into the
air, its motion as it turns, is clearly more complicated than that of a
non-spinning tossed ball, which moves like a particle.
-
- The centre of mass is an imaginary point where one can assume the entire
mass of the given system or object to be positioned.
-
- Consider a system of N particles of masses m1, m2, m3,------------
mN.
-
- If the external forces acting on the system add up to zero, the centre of
mass moves with constant velocity.
-
- Consider two particles A and B of masses m1 and m2,
respectively. Take the line joining A and B as the X-axis. Let the coordinates
of the particles at time 't' be x1 and x2.
-
- The centre of mass of a rigid body is a point whose position is fixed with
respect to the body as a whole. The point may or may not lie in the body. The
position of the centre of mass of a rigid body depends on.
-
- Angular velocity of a rotating rigid body is the rate of change of angle
swept.
-
-
- Angular momentum bears the same relation to linear momentum that torque
does to force.
-
- The angular momentum, which is nothing but moment of linear momentum, can
be expressed in terms of the lever arm for momentum.
-
- We already know two powerful conservation laws, namely, the conservation
of energy and the conservation of linear momentum. Let us study another
conservation law, namely the law of conservation of angular momentum.
-
- Let us consider a student seated on a stool that can rotate freely about a
vertical axis. The student, who is set into rotation at a modest initial
angular speed wi, holds two dumbbells in an outstretched hand. His angular
momentum lies along the vertical rotation axis, pointing upwards.
-
- In the case of a planet, moving around the sun in an elliptical orbit with
the sun at one of the foci of the ellipse, the gravitational force always acts
along the line joining the planet with the sun.
-
- A rigid body is said to be in equilibrium if, both the linear and angular
momentum of a rigid body have a constant value. For the equilibrium of a rigid
body, the body need not be at rest. However, if it is at rest, it is called
the static equilibrium.
-
- Consider a pulley fixed at a typical Indian well on which a rope is wound
with one end attached to the bucket. When the bucket is released, the pulley
starts rotating. As the bucket goes down, the pulley rotates more rapidly till
the bucket goes into the water.
-
- When a rigid body such as a merry-go-round rotates around an axis, each
particle in the body moves in its own circle around that axis. Since the body
is rigid, all particles make one revolution in the same amount of time. i.e.,
they all have the same angular speed w.
-
- Consider a rigid body rotating about a fixed axis AB. Consider a particle
'p' of mass 'm' rotating in a circle of radius 'r'.
-
- It is the distance from the axis of rotation at which, if the whole mass
of the body were to be concentrated, the moment of inertia would be the same
as that with the actual distribution of mass. It is denoted by K.
-
- If a body is assumed to be continuous, one can use the technique of
integration to obtain its moment of inertia about a given line.
-
- The moment of inertia of a body about an axis is equal to its moment of
inertia about a parallel axis through its centre of gravity plus the product
of the mass of the body and the square of the perpendicular distance between
the two parallel axes.
-
- This is applicable only to a plane lamina. The moment of inertia of a
plane lamina about an axis perpendicular to its plane is equal to the sum of
the moments of inertia of the lamina about any two mutually perpendicular
axes, passing in its own plane, intersecting each other at the point through
which the perpendicular axis passes.
-
- The weight Mg of the cylinder, acting vertically downwards through the
centre of mass of the cylinder.
-
- A binary system is one in which two heavenly bodies revolve about a common
centre of mass. (The word binary means two).
-
- In stable equilibrium position, the two atoms in a diatomic molecule are
separated by a certain distance r0. This distance is called
intermolecular distance or bond length.
-
- Principle of conservation of linear momentum states that the linear
momentum of a system remains constant if the external forces acting on the
system add up to zero.
Gravitation
Astronomy has been a fascinating subject from ancient times. The geocentric
system (around the 2nd century A.D.) considered the Earth to be at the centre
with the sun and other planets revolving around it.
-
- Astronomy has been a fascinating subject from ancient times. The
geocentric system (around the 2nd century A.D.) considered the Earth to be at
the centre with the sun and other planets revolving around it.
-
- Every particle of matter in the universe attracts every other particle
with a force which varies directly as the product of their masses and
inversely as the square of the distance between them.
-
- Bodies allowed to fall freely were found to fall at the same rate
irrespective of their masses (air resistance being negligible). The velocity
of a freely falling body increased at a steady rate i.e., the body had
acceleration. This acceleration is called acceleration due to gravity - 'g'.
-
- The space around a body within which its gravitational force of attraction
is experienced, is called its gravitational field.
-
- The work done in moving a unit mass from infinity to a point in a
gravitational field is called the gravitational potential at that point.
-
- The mass of a body can be determined by measuring the acceleration 'a'
produced in it by a known force 'F'.
-
- The moon is a natural satellite of the Earth. We now have a number of
artificial satellites (man-made) revolving around the Earth.
-
- The path of each planet around the sun is an ellipse with the sun at one
focus.
-
- The difference between the gravitational force and the centripetal force
acting on our body is equal to our weight.
-
- Let m1 and m2 be the masses of two bodies separated
by a distance d.
-
- Every particle of matter in a body is attracted to the Earth and the
result of all these attractive forces is the weight of the body.
-
- The Cavendish balance consists of a light, rigid T-shaped member supported
by a fine vertical fibre. Two small spheres of masses m are mounted at the
ends of the horizontal portion of the T. A mirror M on the vertical reflects
the beam of light on to a scale.
-
- The discovery of gravitation by Sir Isaac Newton, due to his observation
of the falling apple, explained the movements of planets and satellites not
only in our solar system but also in other systems as well. It explained why
the Earth and other planets where spherical or nearly spherical in shape.
Mechanics of Solids and Fluids
A spider web is stronger than steel of the same thickness. Its elastic limit
is greater than that of steel.
-
- A spider web is stronger than steel of the same thickness. Its elastic
limit is greater than that of steel.
-
- When two wet glass plates are pressed together, they cannot be separated
easily. This is because of the force of attraction existing between the atoms
and molecules, and are electrical in origin.
-
- Solids have definite shape and volume because the average distance between
the molecules or atoms remain constant and do not change with time. The
arrangement of molecules inside a solid differ from one to another.
-
- External forces acting on a body, bring about a change in its state or
configuration. The latter is possible when the body is not free to move, but
the molecules are compelled to change their positions. Such forces are called
deforming forces.
-
- Elastic bodies regain their original shape due to internal restoring
forces. This internal restoring force, acting per unit area of a deformed
body, is called a stress.
-
- The change in configuration of a body depends on the type of stress. The
ratio of change in configuration to the original configuration is called a
strain. Strain, being a ratio, does not have any units or dimensions.
-
- Experimental study by Hooke revealed that elastic bodies regain their
original configuration completely, only upto a limit. He termed this limit as
the elastic limit. He found that within the elastic limit, the extension
produced in the wire was directly proportional to the load applied.
-
- Corresponding to the three types of strains, there are three types of
modulus. Young's Modulus of elasticity.
-
- Mechanical properties like strength, stiffness (Rigidity), ductility,
malleability and brittleness have to be carefully studied to select a material
for a particular job.
-
- Fluids are substances which begin to flow when external force is applied
on them. Liquids and gases are fluids. Fluids do not have a definite shape.
The branch of physics, dealing with the study of fluids at rest is called
hydrostatics.
-
- Pins and nails have pointed ends so that, when a pin is pressed, high
pressure is applied on the surface with lesser force, as area is small.
-
- Blaise Pascal, a French physicist, discovered that the pressure in a fluid
in equilibrium is the same everywhere, if the effect of gravity is neglected.
-
- A hydraulic lift is used to lift heavy loads. It consists of two pistons
of varying cross-sectional area. The two pistons are connected to each other
with a horizontal pipe.
-
- An iron needle sinks in water but a huge ship floats on the surface of
water.
-
- Let W = Vrg be the true weight of body, acting through the centre of
gravity and let 'w' be the weight of the liquid displaced, acting through the
centre of gravity of the displaced liquid (called the centre of buoyancy).
-
- A floating ship displaces water equal to its own weight, including that of
cargo.
-
- When two solid surfaces slide over each other, a frictional force acts
between them that opposes the relative motion of the bodies. Similarly, when a
layer of a liquid slips on another layer the two exert a tangential force on
another. This opposes their motion. The property of a liquid by virtue of
which, a tangential force acts so as to oppose relative motion between its
layers, is called viscosity.
-
- In the streamline flow of a liquid, every particle of the liquid follows
the same path as the preceding particle. So, it has the same velocity (in
magnitude and direction) as the preceding particle. The path of the particle
is either straight or curved. Crowding of the paths or streamlines, indicates
greater velocity of the liquid particles.
-
- Critical velocity is the velocity of a liquid flow upto which its flow is
streamlined and after which its flow becomes turbulent.
-
- When small spherical bodies move through a viscous medium, the bodies drag
the layers of the medium that are in contact with them. This dragging results
in relative motion between different layers, which are away from the body.
Therefore, a viscous drag comes into play, opposing the motion of the body. It
is found that this backward force or viscous drag, increases with increase in
velocity of the body.
-
- Consider a non-viscous liquid in streamline flow through a tube AB, of
varying cross-section. Let A1 and A2 be the area of
cross-section at A and B respectively.
-
- This theorem is a consequence of the principle of conservation of energy,
applied to ideal liquids in motion.
-
- When we blow air over a strip of paper as shown in the above figure, we
find that the paper moves up. This is because, on blowing air, the velocity of
air increases, creating low pressure above the paper and high pressure below
the paper.
-
- When a thermometer is dropped accidentally, we find the mercury inside the
bulb of the thermometer rolling down as small perfect spheres. Raindrops and
soap bubbles are also perfectly spherical in shape. A plastic strainer floats
on water which is unusual.
-
- It is a property by virtue of which, the free surface of a liquid
possesses a tendency to contract so as to acquire a minimum surface area.
-
- Liquids, according to the Molecular theory, are made up of molecules. Let
KLMN represent a surface film of thickness LM, which is same as the molecular
range. Consider three molecules A, B, C at different positions.
-
- We know that work has to be done in order to bring a molecule, from
interior to the surface, against the force of cohesion. If the surface area is
increased, more molecules can be accommodated at the surface. Increase in
surface area, results in cooling. To maintain the temperature, heat flows from
the surroundings to the film and this is added on. This additional energy is
termed as 'surface energy'.
-
- Surface tension of soap solution is less, it can spread over large areas
and wash clothes more effectively, since the dirt particles stick to the soap
molecules.
-
- The presence of impurities either on the surface or dissolved in it,
affect surface tension of the liquid. Highly soluble substances increase the
surface tension of water, whereas sparingly soluble substances reduce the
surface tension of water.
-
- When one end of a glass capillary tube that is open at both ends, is
dipped in a liquid like water that wets the tube, the liquid level in the tube
rises to a certain height above the liquid level in the container, as shown
below.
-
- The above figure shows two liquids, one liquid which wets the glass and
the other (i.e. diagram 'b') which does not wet the glass. In the first case,
the force of adhesion (i.e. force of attraction between unlike molecules) is
more than the force of cohesion (i.e. force of attraction between like
molecules).
-
- The free surface of a liquid called meniscus, assumes a flat, convex or
concave shape, depending on the solid and liquid surface.
Heat and Thermodynamics
Heat is a form of energy. Heat energy is also called thermal energy. When
heat is given to a body, its temperature increases and when heat is removed from
a body, its temperature decreases.
-
- Heat is a form of energy. Heat energy is also called thermal energy. When
heat is given to a body, its temperature increases and when heat is removed
from a body, its temperature decreases.
-
- This theory explains the physical properties of matter in terms of motion
of its molecules. According to this theory, every substance (solid, liquid or
gas) consists of a large number of minute particles called molecules. A
molecule may be defined as the smallest particle of a substance that can exist
in free state and has all the characteristics of the present substance.
-
- All the molecules of a gas are identical with respect to their shape and
mass. The molecules of different gases are different.
-
- Consider an ideal gas enclosed in a cubical vessel of edge L. Take a
corner of the vessel as the origin O and the X-,Y-, Z- axes along the edges
(figure 1). Let A1 and A2 be the parallel faces, perpendicular to the X-axis.
-
- Let us consider one-gram molecule (mole) of the gas. Let M and V be its
mass and volume respectively.
-
- The total translational energy of all the molecules of the gas
-
- We know that a hotter body has greater internal energy than a similar
colder body. Thus, higher temperature means higher internal energy and lower
temperature means lower internal energy.
-
- At a given temperature, the pressure of a given mass of a gas is inversely
proportional to its volume.
-
- We are now in a position to write the rms speed of the molecules in terms
of the absolute temperature.
-
- The rms speed of an oxygen molecule in a sample at 300 K is about 480m/s.
This does not mean that the speed of each molecule is 480 m/s. Many of the
molecules have speed less than 480m/s and many have speed more than 480m/s.
Maxwell derived an equation giving the distribution of molecules in different
speeds.
-
- The total number of possible independent ways in which the position and
configuration of a mechanical system may change, is the degrees of freedom of
that system.
-
- In 1798, Count Rumford observed that the amount of heat produced is
proportional to the amount of mechanical work done. Later, Dr. James Prescott
Joule of Manchester, established a definite relation between the work done and
the heat produced. It was shown that when a certain amount of mechanical work
is done, an equivalent amount of heat is always produced.
-
- Internal energy is one of the most important concepts in thermodynamics.
Energy changes in a body sliding with friction. Warming a body increases its
internal energy and cooling the body decreases its internal energy.
-
- We have seen that heat is just a form of energy. A system can be given
energy either by supplying heat to it (by placing it in contact with a hotter
object) or by doing mechanical work on it. Consider an ideal gas in a
cylindrical container, fitted with a piston as shown in the figure given
below.
-
- The heat capacity C of an object, is the proportionality constant between
the heat Q that the object absorbs or loses and the resulting temperature
change DT of the object.
-
- Two objects made of the same material, say marble, would have heat
capacities proportional to their masses. It is therefore convenient to define
a “heat capacity per unit mass” or specific heat that refers not to an object
but to a unit mass of the material of the object.
-
- Let us consider one mole of an ideal gas enclosed in a cylinder fitted
with an airtight and frictionless piston. Let P, V and T be the pressure,
volume and absolute temperature of the gas respectively.
-
- In 1819, two French physicists Dulong and Petit discovered that the
average molar specific heat at constant pressure for all metals, except the
very light ones, is approximately the same and equal to nearly 25 J mole-1 oC-1.
-
- Thermodynamic variables are the quantities like pressure, volume and
temperature, which help us to study the behavior of a thermodynamic system.
There are some other thermodynamic variables such as entropy, internal energy,
etc., but these thermodynamic variables can be expressed in terms of pressure,
volume and temperature.
-
- Another simple equation of state is the one for an ideal gas. The figure
below shows an experimental setup to study the behavior of a gas. The cylinder
has a movable piston to vary the volume, heating can vary the temperature, and
we can pump the desired amount of any gas into the cylinder.
-
- In this section, we describe four specific kinds of thermodynamic
processes that often occur in practical situations. These can be summarized
briefly as "no heat transfer" or adiabatic, "constant volume" or isochoric,
"constant pressure" or isobaric, and "constant temperature" or isothermal. For
some of these, we can use a simplified form of the first law of
thermodynamics.
-
- In 1824, a French scientist N.L.Sadi Carnot, suggested an idealized engine
which is called the Carnot engine, which has an intimate relation with the
second law of thermodynamics.
-
- A heat engine takes heat from a hot body, converts a part of it into work
and rejects the rest to a cold body. A refrigerator also known as a heat pump,
does the reverse operation.
-
- Experimental evidence suggests strongly that it is impossible to build a
heat engine that converts heat completely to work (an engine with 100% thermal
efficiency).
-
- We know that there is a transfer of energy, as heat, between a system and
its environment. Here we discuss how this transfer takes place. There are
three mechanisms of heat transfer. They are conduction, convection and
radiation.
-
- Steam is passed into the steam chamber and a stream of water is
maintained. The temperatures of all the four thermometers rise initially and
ultimately become constant when the steady state is reached. The readings q1, q2, q3, and q4
are noted in steady state.
-
- A body that is a good radiator (or emitter) is also a good absorber. To
understand this, suppose isotropic (i.e., equal in all directions) thermal
radiation is incident on a body.
-
- The energy of thermal radiation emitted per unit time by a black body of
surface A.
-
- The rate of loss of heat by a body is directly proportional to the
temperature difference between the body and the surroundings, provided the
difference is not very large.
-
- The solar constant is defined as the amount of heat energy received per
second per unit area by a perfect black body placed at the surface of the
Earth with its surface being held perpendicular to the direction of the sun's
rays.
Oscillations
Oscillatory motion, or periodic motion, is the most common type of motion.
Heartbeat of animals, the seasons of the year, the swinging of the pendulum of a
clock and the vibrations of atoms in solids are periodic in nature.
-
- Oscillatory motion, or periodic motion, is the most common type of motion.
Heartbeat of animals, the seasons of the year, the swinging of the pendulum of
a clock and the vibrations of atoms in solids are periodic in nature.
-
- In the preceding sections, the motion of a body when acted upon by a
constant force was considered. The motion is one of constant acceleration.
-
- The body returns to a given point in the path with the same velocity after
regular intervals of time.
-
- The maximum displacement of the particle executing SHM from the
equilibrium position is known as the amplitude. It will be equal to the radius
of the circle of reference. Therefore, the total range of motion is 2A.
-
- The foot of the perpendicular drawn from the body onto any diameter
executes SHM.
-
- A body moving along a circular path is acted upon the centripetal
acceleration.
-
- The force constant of the spring (or any other agency) which supplies the
restoring force.
-
- To cause a displacement of a body controlled by elastic forces, work has
to be done. For example, work has to be done in stretching a spring against
the elastic forces. This work will be stored in the body as potential energy.
When the deforming force is released, this potential energy manifests in the
form of kinetic energy which makes the body to move. Thus, a body in SHM, has
both potential energy and kinetic energy.
-
- Consider the case when a body moving in a circular path is not at Qo
but at Q when t = 0.
-
- A simple pendulum is an arrangement in which a point mass is suspended by
an inextensible weightless string in a uniform gravitational field. This is an
ideal system which cannot be realized in practice. However, a pendulum
consisting of a small but relatively heavy bob on one end of a very light
string can be considered as a simple pendulum.
-
- An oscillator, in actual practice, almost always lies in a resisting
medium, like air, oil etc., where part of its energy is dissipated in
overcoming the opposing frictional or viscous forces and its amplitude,
therefore, goes on decreasing progressively. Such forces, which are
non-conservative in nature, have thus a damping, resistive or dissipative
forces.
-
- Some objects have a wide range of lengths in the universe.
Waves
Very often, energy is generated at one place but consumed elsewhere. The
transportation of energy from its source to the receiving end can be done in two
ways: By actually moving the matter carrying kinetic energy and delivering it to
the other end.
-
- Very often, energy is generated at one place but consumed elsewhere. The
transportation of energy from its source to the receiving end can be done in
two ways: By actually moving the matter carrying kinetic energy and delivering
it to the other end.
-
- One of the familiar types of waves is the wave on the surface of water.
Let a pebble (P) be dropped gently on the calm surface of water in a pond.
Before the pebble is dropped the surface of water is flat. When the pebble
falls, it pushes the water under it, downwards. Water, being practically
incompressible, gets displaced and rises up all-around in a ring. The pebble
passes through water and reaches the bottom of the pond.
-
- Mechanical wave motion can be defined as the propagation of a disturbance
through a material medium due to the repeated periodic motion of the particles
of the medium about their mean positions, the disturbance being handed over
from one particle to the next.
-
- In this type of wave motion, the particles of the medium vibrate at right
angles to the direction of propagation of the wave.
-
- On observing waves, it may be observed that they travel with a definite
speed through a uniform medium. If we watch a particular spot, we find that
the waves pass that spot at regular intervals of time. The following
definitions help in describing wave motion.
-
- Wave motion is the propagation of a disturbance produced in a medium by
the repeated periodic motion of the particles of the medium.
-
- The simplest type of wave is the one in which the particles of the medium
are set into simple harmonic vibrations as the wave passes through it. The
wave is then called a simple harmonic wave.
-
- In all progressive waves, energy travels through the medium in the
direction in which the wave travels. Each particle of the medium has energy of
vibration and passes energy on to succeeding particles.
-
- When a number of similar waves pass through a medium simultaneously, each
wave travels through the medium as though the others were not present.
-
- Let two similar waves of amplitudes A1 and A2 having
same frequency and wavelength travel past a point in a medium, producing
individual displacements y1 and y2.
-
- It has already been proved that the intensity of a wave is proportional to
the square of the amplitude. At a point where constructive interference has
occurred, the intensity will be maximum and the amplitudes of the two waves
will have added.
-
- Interference of sound waves can be demonstrated using Quincke's tube. It
consists of two U-tubes ABCDE and FGH, whose limbs can be inserted
telescopically into each other.
-
- Stationary or standing waves are formed in a medium when two waves having
equal amplitude and frequency moving in opposite directions along the same
line, interfere in a confined space. Generally, such waves are formed by the
superposition of a forward wave and the reflected wave. Both longitudinal and
transverse types of waves can form a stationary wave.
-
- In this case, there will be no reversal of phase due to reflection.
-
- In stationary waves, there are certain points called nodes where the
particles are permanently at rest and certain other points called antinodes
where the particles vibrate with maximum amplitude. The nodes and antinodes
are formed alternately.
-
- The disturbance produced in the medium travels onward, it being handed
over from one particle to the next. Each particle executes the same type of
vibration as the preceding one, though not at the same time.
-
- An organ pipe is the simplest form of a wind instrument. Figure (a) shows
the longitudinal section of an organ pipe whose one end is closed and figure
(b) shows an organ pipe, both ends of which are open. It consists of a hollow
tube BD in which air can be blown through a pipe A (also called the
mouthpiece).
-
- A mechanical system which is free to vibrate like a hacksaw blade clamped
at one end, a diving spring board or the air in pipes has a natural frequency
of vibration f0, which depends on its dimensions. When a periodic
force of a frequency different from f0 is applied to the system, it
vibrates with a small amplitude and undergoes forced vibrations.
-
- In physics, the word 'string' is used in a more general sense than what it
normally denotes. In olden days, musical instruments employed strings of
twisted intestines of animals, such as cat-gut. Nowadays, the strings of
musical instruments like the veena, violin and guitar are made of metal wires.
-
- A sonometer, also called a monochord, was invented by Pythagoras (580-500
B.C.). It is a simple instrument used to verify the laws of stretched strings
and to determine the frequency of a tuning fork. It consists of a long hollow
rectangular wooden box (w) called the sound box, having three openings on one
of its sides.
-
- Melde's electrically maintained tuning fork consists of a large tuning
fork (F) made of a ferromagnetic alloy, whose shank is rigidly clamped to a
heavy rectangular wooden board (W).
-
- Mechanical waves which can cause the sensation of hearing are called sound
waves. These waves are produced by bodies vibrating at frequencies lying
between the range of 20Hz and 20,000Hz, perceived by the human ear.
-
- Ordinarily, we hear sound, transmitted through the air. Unlike light,
sound cannot pass through vacuum. This was discovered in 1654 by Otto Von
Guericke.
-
- The restoring force acting on the particles of the medium is intimately
connected to the approximate elastic modulus of the medium and the inertial
mass, to its density.
-
- Assuming isothermal conditions to prevail when sound travels through air,
Newton has applied Boyle's law to the changes in pressure and volume.
-
- As seen from equation (1-28), the velocity of sound in a gas depends on g, the ratio of the principle specific heats of the
gas. This, in turn, depends on the atomicity of the gas.
-
- The velocity of sound in water was determined by Daniel Colladon and Jacob
Sturm in the lake of Geneva in 1827.
-
- Physically, a wave involves the propagation of energy. This transfer of
energy by a traveling wave is expressed in terms of the intensity I. Intensity
of sound waves is defined as the average energy transported per second per
unit area perpendicular to the direction of propagation. It is measured in Js-1m-2
or Wm-2.
-
- The loudness of sound depends upon both intensity and frequency. For a
given frequency, an increase in intensity produces an increase in loudness,
but the sensitivity of the ear is so different in the various frequency ranges
that equal intensities produce far different sensations in the different
regions.
-
- A musical instrument like a guitar or veena gives louder sound when its
string is plucked with a greater force. The intensity is directly proportional
to the square of the amplitude of vibration of the source. The loudness which
is a logarithmic function of intensity, also increases.
-
- As the threshold of audibility varies with frequency, sounds of the same
intensity but different frequencies are found to differ in loudness.
Therefore, another unit of loudness is defined. This unit measures the
intensity of a sound relative to a reference tone of defined pressure and
frequency.
-
- Audible sounds are classified into two groups, namely musical sounds and
noise. A musical sound is that in which the vibrations of the sounding body
are periodic, follow each other regularly and rapidly, so as to produce a
pleasing effect on the ear without any sudden change in loudness.
-
- Whenever two wave motions pass through a single region of a medium
simultaneously, the motion of the particles in the medium will be the result
of the combined disturbance due to the two waves. This effect of superposition
of waves, is also known as interference.
-
- Let a stationary observer on a platform listen to the sound emitted by the
whistle of an incoming train. As the train approaches the platform, an
increase in the pitch of the sound will be observed.
-
- Observer and source moving in the same direction as sound in a stationary
medium.
-
- The Doppler effect can be observed in all kinds of waves so long as the
speed of the source is small when compared to the speed of the wave.
-
- The Doppler effect provides a convenient means of tracking a satellite
that is emitting a radio signal of constant frequency. The frequency of the
signal received on the Earth changes as the satellite is passing.
-
- An auditorium is a part of a building in which large number of people may
be seated to listen to a speech or music. It is not uncommon to find an
auditorium, which may be an architectural masterpiece but falls below
standards on acoustic considerations.
-
- The persistence of audible sound even after the source has ceased emitting
sound is called reverberation.
-
- Prof. Wallace C. Sabine (1868 - 1919) of Harvard University investigated
architectural acoustics scientifically, particularly with reference to
reverberation time.
-
- All vibrating and oscillating bodies are described by the length of time
required for one complete cycle.
Electric Charges and Field
The word 'electric' is derived from the Greek word 'elektron' meaning amber.
The existence of charges were known when charged particles were produced by
rubbing (due to friction) of suitable materials. These facts are demonstrated by
simple experiments.
-
- The word 'electric' is derived from the Greek word 'elektron' meaning
amber. The existence of charges were known when charged particles were
produced by rubbing (due to friction) of suitable materials. These facts are
demonstrated by simple experiments.
-
- It is important to know the atomic picture of matter. The basic unit of
all matter is an 'atom'. Each atom consists of a small core called nucleus
which accounts to most of its mass consisting of positively charged protons
and neutral neutrons and surrounded by lighter negatively charged particles
called electrons.
-
- A charged plastic rod is brought close to the sphere. Free electrons in
the sphere move away due to repulsion and piles up at the other end of the
sphere.
-
- It states that "the electrostatic force between two electric charges is
directly proportional to the product of the charges and inversely proportional
to the square of the distance between them ".
-
- If a system consists of two point charges q1 and q2,
then the total charge of the system is got by adding q1 and q2.
Thus, the charge add up like real numbers (scalars). When we add charges, one
should take care of its sign.
-
- Coulomb's law describes only the interaction of two point charges.
Experiments show that when two charges exert forces simultaneously on a third
charge, the total force acting on that charge is the vector sum of the forces
that the two charges would exert individually. This important property is
known as the superposition principle. This principle holds good for any number
of charges.
-
- The electric field or electric field strength is the electrostatic force
acting on a small positive test charge placed at that point.
-
- It is a pair of point charges with equal magnitude and opposite in sign
separated by a distance.
-
- An electric field is said to be uniform if the electric field strength at
every point in the field is the same.
-
- They are nothing but a way of pictorially mapping the electric field
around a configuration of charges. It is the curve drawn in such a way that
the tangent to it at each point is in the direction of the net field at the
point. An arrow on the lines of force is a must to indicate the direction of
the electric field.
-
- Electric field can be quantitatively described by using the concept of
electric flux.
-
- We have already learnt to find the electric field intensity due to a
charged conductor using Coulomb's law. Gauss' theorem can also be used to
calculate the electric field intensity provided there is a symmetry in the
charge distribution.
-
- We have so far dealt with discrete charges but a system of charges can be
considered as a continuous distribution if the group of charges are located
very close together. To find the electric field due to a continuous charge
distribution we have to define the following terms.
-
- Gauss' theorem can be used to calculate the electric intensity due to an
infinitely long straight charged wire.
-
- Conductor allow flow of electric charges through them while insulators
don't.
-
- Principle of electrostatics and electromagnetism play a very vital role in
all modern scientific developments.
-
- Two identical balls, each of mass 0.1 x 10-3 kg, carry
identical charges and are suspended by two threads of equal length. At
equilibrium, they position themselves as shown in the figure below. Calculate
the charge on either ball.
-
- Calculate the resultant force on the 10 microcoulomb of charge.
-
- Find the force on the centre charge.
-
- he charges shown in the figure are stationary. Find the force on 4mC
charge due to the other two.
-
- n a hydrogen atom, the distance between electron and proton is 5.3 x 10-11
m. Calculate the electrical force of attraction between them.
Electrostatic Potential and Capacitance
Just as the electric field is described as force per unit charge, electric
potential at a point can be described as electrical potential energy per unit
charge.
-
- Just as the electric field is described as force per unit charge, electric
potential at a point can be described as electrical potential energy per unit
charge.
-
- Consider two points 'a' and 'b' in an electrostatic field of a single
isolated point charge +q.
-
- The potential at point P is the algebraic sum of the potentials due to -q
and +q charges.
-
- Potential at a point due to a system of charges is the sum of potentials
due to individual charges.
-
- Electrostatic field lines help us visualize electric fields. Similarly,
potential at various points in an electric field can be represented
graphically by equipotential surfaces.
-
-
- Consider an external electric field 'E' produced by an external source,
where it can specified or unspecified. But the potential 'V' due to external
source has to be specified.
-
- All materials are broadly classified into two categories, one conductors
and other insulators. When a conductor is placed in a electric field, there is
a large scale of physical movement of free electrons, within the conductor and
they move out only if we make arrangements for it.
-
- It consists of two conducting plates parallel to each other and separated
by a distance 'd', which is small when compared to the length of the plates.
-
- The potential difference across each capacitor however is different.
-
- While charging a capacitor, a battery transfers positive charge from
negative to the positive plate. So some work is done in transferring this
charge, which is stored in the capacitor in the form of electrostatic energy.
-
- Dielectrics are non-conducting substances, they have no charge carriers or
no free electrons. If an external field is applied, it turns out that charges
are induced on the surface which in turn produces a field and opposes the
external field. The opposing field does not exactly cancel the external field
but only reduces it.
-
- Capacitance of Parallel Plate with a Dielectric Slab.
-
- Action of sharp points: Charges are leaked from pointed ends of charged
conductors. This creates an electric wind (as moving air is ionized) which
moves away from the conductor.
-
- Capacitance of a parallel plate on introducing a dielectric slab (er)
of thickness t.
-
- Potential Energy: is the work done at a point by an external agent in
moving a unit positive charge from infinity to a given point against the
electrostatic field.
-
-  There has been considerable development in our day to day life due to
study and application of Conductors, Insulators, and Capacitors.;
-
- Calculate the absolute potential at the point P.
-
- Eight charges having the values shown in figure are arranged symmetrically
on a circle of radius 0.4 m in air. Calculate the potential at the centre O.
-
- If a piece of metal has a charge +0.1mC and is placed inside a hollow
metal sphere of radius 20 cm (with touching it), what is the potential of the
sphere? What will the potential of the sphere become, if a) the sphere is
temporarily Earthed and then left insulated?
-
- Charges of +20 esu, +9 esu and -5 esu are placed at the corners A, B and C
respectively of a DABC shown in the figure. Calculate the potential at the
midpoint O of BC.
-
- Calculate the potential at the centre O of the square.
-
- Calculate the potential at P due to the charge configuration shown in the
figure. If r>>a, then how will you modify the result?
-
- Calculate the area of the plate of one Farad parallel plate capacitor if
the separation between the plates is one millimetre and plates are in vacuum.
-
- 0.5 F capacitor is placed parallel with 0.75 F capacitor and the
combination is joined by 110 V DC source. Calculate the charge from the source
and charges on each capacitor.
-
- Assume the radius of electron same to the radius of proton which is 10-15
m. Let the electron charge reside on the surface. What is the potential energy
of such as charge distribution? Also, calculate the relativistic mass
equivalent of this energy.
-
- A parallel capacitor of plate area 2m2 and plate separation 5
mm is charged to 10,000 V in free space. Calculate (a) capacitance (b) Charge
(c) Charge density (d) Field intensity (e) Field displacement.
Current Electricity
Electric current is a means by which electrical energy is transferred from
one place to another for utilisation. Charges in motion constitute an electric
current.
-
- Electric current is a means by which electrical energy is transferred from
one place to another for utilisation. Charges in motion constitute an electric
current.
-
- A current is any motion of charge from one region to another. The
illustration below shows two bodies at different potentials. When these are
connected with a wire, free electrons flow from B to A until both bodies
attain the same potential, after which the current ceases to flow. Current
flows if a potential difference exists throughout a conductor. This branch of
physics dealing with charges in motion is called current electricity.
-
- No current flows in a copper wire by itself, just as water in a horizontal
tube does not flow. If one end of the tube is connected to a tank with water
such that there is a pressure difference between the two ends of the
horizontal tube, water flows out of the other end at a steady rate.
-
- It is found experimentally that the current I flowing through a conductor
is directly proportional to the potential difference V across its ends,
provided the physical conditions (temperature, mechanical strain, etc.,)
remain constant.
-
- In electrostatic situations, the electric field is zero everywhere within
the conductor, and there is no current. This does not mean that all charges
within the conductor are at rest.
-
- The resistivity of a metallic conductor nearly always increases with
increasing temperature.
-
- Ohm's law is not a fundamental law of nature. There are a number of
commonly used circuit elements which do not obey this law.
-
- Some materials, including several metals and alloys, exhibit a phenomenon
called superconductivity.
-
- When resistors, can be connected in such a way that the same current flows
in them, then they are said to be connected in series. The resistors are said
to be connected in parallel if the potential difference is the same across
each resistor.
-
- In many electrical circuits, Ohm's law cannot be applied. This happens
when there is more than one source of emf in the circuit or when resistors are
connected in a complicated manner. To solve such complex circuits, Gustav
Robert Kirchhoff developed two laws based on charge neutrality in a metal.
-
- These devices measure the voltage and current respectively in a circuit.
The basic component of both is the moving coil galvanometer which produces a
deflection proportional to the electric current through it.
-
- This is the simplest form of wheatstone bridge and is specially useful for
comparing resistances more accurately.
-
- Current through a given area of a conductor is the net charge passing per
unit time through the area.
-
- In the case of hydrogen atom, an electron moves in an orbit of radius 5x10-11
m with a speed of 2.2 x 106 ms-1. Calculate the
equivalent current. Given: charge on an electron = 1.6 x 10-19C.
-
- How many electrons flow through the filament of a 120 V, 60 W electric
lamp in one second? Given: Electric power is the product of voltage and
current.
-
- What is the number of free electrons in a piece of silver of cross-section
1.0 x 10-4 m2 and length 1m? Atomic weight of silver =
108, density of silver = 105 x 102 kg m-3. Assume that
there is one free electron per atom.
-
- What is the drift velocity of electrons in a copper conductor having a
cross-sectional area of 5 x 10-6 m2 if the current is
10A? Assume that there are 8 x 1028 electrons/m3A.
-
- Calculate the drift velocity of electrons in a silver wire having
cross-sectional area of 3.14 x 10-6 m2 and carrying a
current of 20 amperes. Given: Avogadro's number = 6.023 x 1023,
atomic weight of silver = 108. Density of silver = 10.5 x 103 kg m-3,
e = 1.6 x 10-19C.
-
- A car has a fresh storage battery of EMF 12V, internal resistance 5.0 x 10-2 W. If the starter motor draws a current of 90 A, what
is the terminal voltage of the battery when the starter is on?
-
- Two identical cells of EMF 1.5 V each joined in parallel provide supply to
an external circuit consisting of two resistors of 17W
each joined in parallel. A very high resistance voltmeter reads the terminal
voltage of the cell to be 1.4 V. What is the internal resistance of each cell
? (e=1.6 x 10-19C)
Thermal and Chemical Effects of Currents
When a potential difference is applied across the ends of a conductor, the
free electrons are accelerated and acquire kinetic energy. As the electrons move
through, they collide with the positive ions and atoms of the conductor and
transfer their kinetic energy to them.
-
- When a potential difference is applied across the ends of a conductor, the
free electrons are accelerated and acquire kinetic energy. As the electrons
move through, they collide with the positive ions and atoms of the conductor
and transfer their kinetic energy to them.
-
- This heating is inevitable in any electrical circuit. Since the energy
lost by the flowing charges ends up as disorderly thermal motion, the phrase
'ohmic dissipation' is also used to describe it.
-
- The phenomenon of electrolysis is an important chemical effect of electric
current. In a metallic conductor, the electric current is due to the drifting
of free electrons, there is no chemical or physical change, only the
generation of heat.
-
- The mass of a substance liberated or deposited at an electrode during
electrolysis is directly proportional to the quantity of charge passed through
the electrolyte.
-
- The fact that chemical reactions produce electrical effects was discovered
accidentally in 1791 by Luigi Galwani, professor of anatomy at the University
of Bologna, Italy.
-
- The electrodes used in the cells discussed so far, deteriorate with the
passage of current and cannot offer a constant emf indefinitely. However,
there was a few cells called standard cells, which can maintain a fairly
constant emf over very long periods of time compared to the other cells.
-
- Thermoelectricity refers to the phenomena that occur at the junctions of
dissimilar conductors when a temperature difference exists between the
junctions. The same phenomenon occurs within a single conductor too, with the
two ends are maintained at different temperatures.
-
- In 1834, a French scientist Peltier, found an effect that was the converse
of the Seebeck effect.
-
- These are in the measurement of temperature and in thermoelectric
generators and refrigerators.
-
- If a current I flows through a potential drop V, the energy lost per
second by the drifting charges is VI. In a resistor of resistance R, the loss
of energy appears as heat. The rate of heat production P is P = VI = I2R
= V2/R and is independent of the direction of current.
-
- A current of 0.50 ampere is passing through a CuSO4 solution.
How many Cu++ ions will be deposited on cathode in 10 seconds?
-
- Six lead-acid type of secondary cells, each of emf 20 V and internal
resistance 0.015W, are joined in series to provide a
supply to a resistance of 8.5W. Determine (i) the
current drawn from the supply and (ii) it's voltage.
-
- It is desired to deposit 0.254 kg of copper on the cathode of a copper
voltameter. How long will it take to deposit this amount if a steady current
of 100 A is maintained? Use the known value of Faraday's constant. Relative
atomic mass of copper is 63. 5.
-
- A steady current of 10.0 A is passed through a water voltameter for 300s.
Estimate the volume of H2 evolved at standard temperature and
pressure. Use the known value of Faraday's constant. Relative molecular mass
of H2 is 2.016 and molar volume = 22.4 litres (volume of 1m of an
ideal gas at STP).
-
- In a silver-plating system, an electrolysis current of 5.0 A is used for a
certain time and 0.5 moles of silver is deposited. How many moles of copper
and iron will be deposited in their respective plating system if an
electrolysis current of 10.0 A is passed for twice the time for silver
plating?
-
- A piece of metal weighting 200 g is to be electroplated with 5% of its
weight in gold. If the strength of the available current is 2 ampere, how long
would it take to deposit the required amount of gold?
-
- In a given thermocouple, the temperature of the cold junction is 20oC
while the neutral temperature is 270oC. Find the temperature of
inversion.
-
- The temperature qn (neutral
temperature) corresponding to maximum emf.
-
- At room temperature, the thermo emf of a copper constant couple is 40 mV per degree. What is the smallest temperature
difference that can be detected with a single such couple and a galvanometer
of 100 ohm resistance capable of detecting current as low as 10-6
ampere?
-
- A sensitive microphone cannot withstand currents greater than 0.05A. When
connected across a thermocouple of emf 8.5 mV, the current in a very low
resistance ammeter placed in series in the circuit reads 34 mA. Calculate the
resistance of the microphone.
Moving Charges and Magnetism
The branch of physics which deals with magnetism due to the electric current
is called electromagnetism. For a long time it was hard to believe if there
existed a relation between electricity and magnetism.
-
- The branch of physics which deals with magnetism due to the electric
current is called electromagnetism. For a long time it was hard to believe if
there existed a relation between electricity and magnetism.
-
- The Biot - Savart's law enables us to write the general results for the
magnetic field due to an arbitrary current distribution or it is an
experimental law predicted by Biot and Savart dealing with magnetic field
strength at a point due to a small current element.
-
- Consider a straight conductor XY carrying a current I as shown. To find
the magnetic field at P, consider a small current element of length dl.
-
- Ampere's law is a useful relation that is analogous to Gauss's law.
Ampere's law is a relationship between the tangential component of magnetic
field at points on a closed curve and the net current through the area bounded
by the curve.
-
- Toroid is a hollow circular ring (like a medu vadai) on which a large
number of turns of a wire are wound.
-
- The force experienced by a charged particle moving in space where both
electric and magnetic field exist is called lorentz force.
-
- The sub-atomic charged particles experience large forces when subjected to
electric and magnetic fields due to their extremely small mass. In nuclear
physics such energized particles are used to bombard nuclei causing nuclear
reactions. This helps to obtain information about the nucleus.
-
- Force between Two Parallel Conductors Carrying Currents
-
- When an electric current flows in a closed loop of wire, placed in a
uniform magnetic field, the magnetic forces produce a torque which tends to
rotate the loop so that area of the loop is perpendicular to the direction of
the magnetic field.
-
- A moving coil galvanometer is an instrument used for detection and
measurement of small electric currents.
-
- The Biot-Savart law asserts that the magnetic field dB due to an element
dl carrying a steady current i at a point P at a distance r from the current
element.
-
- The magnetic field at the centre of a circular current carrying coil.
-
- Two wires A and B have the same length of 44 cm, and carry a current of 10
A each. Wire A is bent into a circle and wire B is bent into a square. (a)
Which wire produces a greater magnetic field at the centre? (b) Obtain the
magnitudes of the fields at the centres of the two wires.
-
- Two concentric circular coils X and Y of radii 16cm and 10cm respectively
lie in the same vertical plane containing the north-south direction.
-
- A solenoid 50cm long has 4 layers of windings of 350 turns each. The
radius of the lowest layer is 1.4cm.
-
- A long straight wire carries a current of 4A. What is the magnetic field
at a point distant 10cm from the wire?
-
- Two concentric circles of radius 2 cm and 4 cm respectively carry currents
of 2A and 4A in a clockwise direction.
-
- A given length L of a uniform wire is bent (i) into a single circular turn
and (ii) into n identical circular turns. What is the ratio of the magnetic
field at the center of the coil in both the cases mentioned above when same
current is passed through them?
-
- In the Bohr model of the hydrogen atom the electron revolves around the
nucleus in a path of radius 5.1 x 10-11 m at a frequency of 6.8 x
1015 revolution per second.
-
- A long, thin straight solenoid has 500 turns wound over a length of 50cm.
It carries a current of 0.5A. What is the magnetic field inside this solenoid?
-
- A straight solenoid has 400 turns wound on a cylinder of radius 5cm and
length 40cm. What is the magnetic field at the mid-point of solenoid when a
current of 2A flows in it?
-
- Two solenoids P and Q have length and the total number of turns in the
ratio of 1:2. What is the ratio of the magnetic field inside the two solenoids
due to the same current?
-
- An electron is projected with a speed of 105ms-1 at
right angles to a magnetic field of 0.019 G. Calculate the radius of the
circle described by the electron.
-
- An electron is accelerated from rest through a potential difference of 3
KV. It enters into the region of a uniform, perpendicular magnetic field of
0.2T. What is the radius of the path of electron inside the field?
-
- A straight horizontal conducting rod of length 0.45 m and mass 60g is
suspended by two vertical wires at it's ends. A current of 5.0 A is set up in
the rod through the wires.
-
- Two straight wires A and B of lengths 10m and 12m carrying currents of
4.0A and 6.0A respectively in opposite directions lie parallel to each other
at a distance of 3.0cm. Estimate the force on a 15cm section of the wire B
near its centre.
Magnetism and Matter
The first magnetic phenomenon observed were those associated with naturally
occurring magnets, fragments of iron ore found near the ancient city of
Magnesia. These attracted unmagnetised iron. The attraction was maximum at
certain regions of the magnet called the poles.
-
- The first magnetic phenomenon observed were those associated with
naturally occurring magnets, fragments of iron ore found near the ancient city
of Magnesia. These attracted unmagnetised iron. The attraction was maximum at
certain regions of the magnet called the poles.
-
- The compass needle always lies along the direction of the field. The
figure below shows the lines or pattern of the field, when the compass needle
is placed at several places. These lines do not really, tell us the effect
that magnet has on the other.
-
- Gauss's theorem in electrostatics indicates that isolated charges exist
and that electric lines of force do not form closed loops. The situation is
different in magnetism.
-
- A magnetic compass was used to help the sailors for navigational purpose.
But recently it has been discovered that some migrant birds have magnetic
sensors in their heads, which help to guide them using the Earth's magnetic
field.
-
- The ultimate source of magnetism is the magnetic dipole moment, associated
with an atom due to orbital motion and intrinsic spin. This suggests that all
substances possess magnetic property as energy material consists of atoms
having electrons revolving around the nucleus.
-
- Michael Faraday discovered that a specimen of bismuth was repelled by a
strong magnet. Diamagnetism occurs in all materials. These materials are those
in which individual atoms do not possess any net magnetic moment.
-
- Materials for making permanent magnet should possess high residual
magnetism i.e., when the magnetising field is reduced to zero, the intensity
of magnetisation is high.
-
- The science of magnetism is old. It has been known since ancient times
that magnetic materials tend to point in the north-south direction: like
magnetic poles repel and unlike ones attract; and cutting a bar magnet in two
leads to two smaller magnets. Magnetic poles cannot be isolated.
-
- A short bar magnet placed with its axis at 300 with a uniform external
magnetic field of 0.16 T experiences a torque of magnitude 0.032 J.
-
- A bar magnet of magnetic moment 1.5 lies aligned with the direction of a
uniform magnetic field of 0.22 tesla.
-
- The radius of the coil of a tangent galvanometer is 0.16 m. How many turns
of the wire should be wound on it if a current of 40 mA is to produce a
deflection of 45o? Given: horizontal component of Earth's field is
0.36 x 10-4T.
-
- A circular coil of 16 turns and radius 10 cm, carrying a current of 0.75 A
rests with its plane normal to an external field of magnitude 5.0 x 10-2
T.
-
- A telephone cable at a place has four long straight horizontal wires
carrying a current of 1 ampere in the same direction east to west. The Earth's
magnetic field at the place is 0.39 gauss, and the angle of dip is 35o.
The magnetic declination is nearly zero.
-
- The core of a toroid having 3000 turns has inner and outer radii of 11 cm
and 12 cm respectively. The magnetic field in the core for a current of 0.70 A
is 2.5 T.
Electromagnetic Induction
We have seen in the previous lesson that a current carrying conductor when
kept in a magnetic field experiences forces and torques.
-
- We have seen in the previous lesson that a current carrying conductor when
kept in a magnetic field experiences forces and torques.
-
- We have already seen how the concept of electric flux helped us to learn
the electric field intensities around the charges. Similarly concept of
magnetic flux too helps us to calculate magnetic field strengths around
magnets or current carrying conductors.
-
- Faraday and Henry performed lots of experiments to learn about the
connection between electricity and magnetism. The results of these experiments
have led to the life styles of todays men, who made life easy by using lots of
electrical applications.
-
- The motion of the magnet in either direction causes a change in strength
of the magnetic field linked with the coil and this causes a current to be
induced in the coil. This induced current opposes the change in the magnetic
field by producing its own magnetic field.
-
- Suppose a uniform magnetic field B perpendicular to the plane of paper
point outward is represented in the region ABCD. A rectangular loop PQRS is
pulled such that it moves with a velocity V.
-
- If the north pole of the magnet is moved towards the coil, the upper
face(U.F) of the magnet acquires the north polarity on closing the key between
2 and 3.
-
- The direction of induced current can easily be predicted using Fleming's
right hand rule.
-
- Induced currents are produced not only in the wires, but also in the block
of metals. If a metallic block is placed in a continuously changing magnetic
field, induced currents are set up in the body of the metallic block.
-
- When a steady current passes through a moving coil galvanometer, the coil
undergoes a torque and does not come to equilibrium position instantly. Hence
the coil is wound over a metallic frame so that the eddy currents produced in
the frame can damp the oscillation and brings the coil to the equilibrium
position instantly.
-
- When a current is established in a conductor, a magnetic field is produced
in its vicinity. We can visualize this field in terms of magnetic flux. If
steady current flows the number of lines of force at a given place would
remain the same.
-
- We know that if a current builds up or varies in a coil, the flux change
leads to induced e.m.f in the same coil. This can happen event mutually
between two interacting coils are close together, and if current is passed in
one of them, it sets up a magnetic flux surrounding itself.
-
- Electromagnetic induction (E.M.I) is the phenomenon of generating EMF by
changing the number of magnetic lines of force associated with a circuit. The
EMF so generated is called induced EMF and the corresponding current is called
induced current.
-
- A loop of wire of area 1m2 is placed perpendicular to a uniform
magnetic field of 1Wbm-2. If the field is uniformly increased to
2Wbm-2 in a time of 10 seconds, find the induced EMF.
-
- A wire 40 cm long bent into a rectangular loop of 15 cm x 5 cm is placed
perpendicular to the magnetic field whose flux density is 0.8Wbm2.
Within 0.5 seconds, the loop is changed into a 10cm square and the flux
density increases to 1.4 Wb m-2. Find the induced EMF.
-
- A circular coil of radius 8.0 cm and 20 turns rotates about its vertical
diameter with an angular speed of 50ms-1 in a uniform horizontal
magnetic field of magnitude 3.0 x 10-2 T.
-
- A copper disc of radius 10 cm rotates 1200 times per minute with its plane
perpendicular to a uniform magnetic field. If the induced EMF between the edge
and centre of disc is 6.284 mV, find the density of the field.
-
- Find the EMF in a coil of 50 turns, each of area 80 cm2 when
making 1800 revolutions per minute in a uniform field of flux density 6 x 10-3
T.
-
- If the coefficient of mutual inductance of the primary and secondary coils
of an induction coil is 6H and a current of 5A is cut off in 1/500 second,
calculate the E.M.F f induced in the secondary coil.
Alternating Currents
Do we use dry cells for operating electrical appliance? It is not impossible
to tap continuous supply of energy from electrochemical cells. Electrical
circuits in homes, factories and offices receive such energy form local power
companies. In most countries the energy is supplied via oscillating e.m.fs and
currents. These oscillating currents are called as alternating currents, shortly
as a.c.
-
- Do we use dry cells for operating electrical appliance? It is not
impossible to tap continuous supply of energy from electrochemical cells.
Electrical circuits in homes, factories and offices receive such energy form
local power companies. In most countries the energy is supplied via
oscillating e.m.fs and currents. These oscillating currents are called as
alternating currents, shortly as a.c.
-
- Let an AC source of EMF E be connected to a pure resistance R. The
instantaneous EMF from the source.
-
- Phasors rotate clockwise about the origin with angular speed equal to the
angular frequency of current and voltage.
-
- Let an AC source be connected across a pure inductive element. If the
alternating current I = Io sin wt flows
through it.
-
- Let an AC source be connected across pure inductive element.
-
- When an AC source is connected in a circuit with a resistance and a
reactance together, the current varies initially in a complex way. After
sufficient time, a sinusoidally varying current persists in the circuit. This
steady state current has a frequency equal to that of the source and may have
a phase difference with the source voltage.
-
- The circuit behaves like a pure resistive one, the current and voltage are
in phase. This fact helps in tuning our TV and radio sets.
-
- In an electrical circuit, energy is supplied by the source of EMF, stored
by the capacitive and inductive elements and dissipated in resistive elements.
-
- Capacitors and inductors are capable of storing energy in the electric
field and magnetic field respectively.
-
- An 'AC generator' or 'dynamo' is a machine which produces AC from
mechanical energy. Actually, it is an alternator which converts one form of
energy into another.
-
- An electrical device is used to change the AC voltage. A transformer which
increases the AC voltage is called a 'step up transformer' and a transformer
which decreases the AC voltage is called a 'step down transformer'.
-
- An alternating current is that which changes continuously in magnitude and
periodically in direction. It can be represented by a sine curve or a cosine
curve.
Optics
It is the phenomenon of change in the path of light without any change in
medium. It is a part of a hollow sphere, whose one side is reflecting and other
side is opaque.
-
- It is the phenomenon of change in the path of light without any change in
medium.
-
- It is a part of a hollow sphere, whose one side is reflecting and other
side is opaque.
-
- These new cartesian sign conventions adopted during measurements.
-
- Consider a ray of light AB, parallel to the principal axis, incident on a
spherical mirror at point B. The normal to the surface at point B is CB and CP
= CB = R, is the radius of curvature.
-
- A formula giving the relation between focal length of the mirror, object
distance, image distance and radius of curvature.
-
- Linear magnification is ratio of the size of the image to the size of the
object.
-
- A convex mirror is used as a rear view mirror in vehicles as images are
small, erect. This gives us a wider view of the traffic behind.
-
- Light not only bounces off surface it goes through some of them often
slowing down and changing direction in the process called refraction. It
occurs at the point where light travels from one medium to another of
different density. Refraction produces mirages and rainbows.
-
- A ray of light incident normally to XY goes undeviated along AB. As the
angle of incidence increases, the angle of refraction also increases.
-
- A refracting surface, which forms a part of a sphere of transparent
refracting material, is called spherical refracting surface. The two types are
convex spherical refracting surfaces and concave spherical refracting
surfaces.
-
- Lens is a portion of transparent refracting medium bound by two spherical
surfaces or one spherical surface and the other plane surface.
-
- This gives the relation between focal length, object distance and image
distance from the optical centre of the lens.
-
- It is a relation that connects focal length of a lens to radii of
curvature of the two surfaces of the lens and refractive index of the material
of the lens.
-
- Convex Lens : Object at Infinity, Object Beyond 2F.
-
- Let two thin lenses L1 and L2 of focal lengths f1
and f2 be placed in contact so as to have a common principal axis.
It is required to find the effective focal length of this combination. Let O
be a point object on the principal axis.
-
- Ability of the lens to converge a beam of light falling on the lens.
-
- A prism is a portion of a transparent medium bounded by two plane faces
inclined to each other at a suitable angle.
-
- It is the phenomenon of splitting of a beam of white light into its
constituent colors on passing through prism. The order of colors from the
lower end are violet, indigo, blue, green, yellow, orange and red.
-
- An optical instrument, which is used for observing pure spectra of sources
of light in the laboratory.
-
- When light emitted from a source is examined directly in a spectroscope,
we observe the emission spectrum of the source.
-
- When light passes through a substance or gas, a part of it is absorbed and
the rest scattered away. The basic process in scattering is absorption of
light by the molecules followed by re-radiation in different directions.
-
- One of the most complicated optical devices is the human eye. Let us see
the construction of the human eye and then the mechanism of image formation.
-
- A photographic camera consists of a converging lens system at least one
end of a box and a light sensitive film at the other end, a focusing device
for adjusting the distance of the lens from the film and an exposure
arrangement which provides the correct exposure.
-
- It consists of a converging lens of small focal length. By keeping the
object close to the lens, a virtual, erect and magnified image is obtained.
-
- It is an optical instrument used for observing highly magnified images of
tiny objects.
-
- An instrument used for observing distinct images of heavenly bodies. In
the normal adjustment, the final image is formed at infinity.
-
- The objective lens is replaced by a concave parabolic mirror of large
aperture. The images in such telescopes are brighter and have a high resolving
power compared to astronomical telescope.
-
- The branch of physics dealing with the study of optical phenomena is
called optics. This can be divided into two categories, ray optics and wave
optics.
-
- Wavefront is the continuous locus of all the particles of a medium that
are vibrating in the same phase. A light source sends out disturbance (waves)
in all the directions.
-
- Huygen proposed a hypothesis for the geometrical construction of the
position of a common wavefront at any instant during the propagations of waves
in a medium.
-
- Consider AB a plane incident wavefront on a mirror M1M2.
Let ÐBAA' = Ði = be the angle
of incidence. Every point on the wavefront AB is a source of secondary
disturbance.
-
- XY is a plane surface separating a denser medium of refractive index from
a rarer medium.
-
- The two short lined waves traveling in opposite direction first add up
(center) to form a resultant wave and then move off as if nothing happened to
them.
-
- Since light has a very small wavelength, we need two slits, which send out
two continuous coherent waves. Since the two slits are placed very close.
-
- In different colors, the fringes have different widths. This indicates
that a relation exists between colour and fringe widths. But before going to
the relation, let us know more about the condition under which constructive
interference or destructive interference occurs.
-
- Let A and B be two fine slits, a small distance 'd' apart. Let them be
illuminated by a monochromatic light of wavelength l.
-
- Diffraction in sound waves and radio waves are readings observed as they
have a relatively longer wavelength compared to light waves.
-
- The ability of the instrument to resolve the images of two point objects
lying close to each other. Due to the wave nature of light each point object
produces its own diffraction pattern, which overlap, and the image can no
longer be identified.
-
- Light is an electromagnetic wave with electric and magnetic field vectors
varying sinusoidally, perpendicular to each other as well as perpendicular to
the direction of propagation of wave of light.
-
- If q is the angle between the plane of
transmission of the analyzer and the polarizer, then intensity of the
transmitted light I
-
- When a beam of white light is passed through a medium containing particles
of size nearly equal to the wavelength of light, the beam gets scattered. This
scattered light is seen in a direction perpendicular to that of incidence and
is found to be plane polarized.
-
- Polaroids are used in sun glasses. They reduce the intensity and the glare
by cutting down the horizontally polarized light.
-
- Whenever there is a relative motion between a source of light and the
observer, the apparent frequency of light received by the observer is
different from the true frequency of light emitted actually from the source of
light.
-
- Ray optics is also called geometrical optics as it uses the geometry of
straight-line paths (rays) to explain the optical phenomena.
-
- Continuous emission spectrum, which contains all the wavelengths in a
particular region. The range of wavelengths emitted depends only on
temperature of the source.
-
- A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length
15cm. Give the location of the image and the magnification. Describe what
happens as the needle is moved farther from the mirror.
-
- A square wire of side 3.0 cm is placed 25 cm away from a concave mirror of
focal length 10 cm. What is the area enclosed by the image of the wire? Given:
The centre of the wire is on the axis of the mirror, with its two sides normal
to the axis.
-
- A small pin fixed on a table top is viewed from above from a distance of
50 cm. By what distance would the pin appear to be raised if it is viewed from
the same point through a 15 cm thick glass slab held parallel to the table?
Refractive index of glass = 1.5. Does the answer depend on the location of the
slab?
-
- A needle placed 45 cm from a lens forms an image on a screen placed 90 cm
on the other side of the lens. Identify the type of lens and determine its
focal length. What is the size of the image if the size of the needle is 5.0
cm?
-
- An object of size 3.0 cm is placed 14 cm in front of a concave lens of
focal length 21 cm. Describe the image produced by the lens. What happens if
the object is moved farther from the lens?
-
- Double convex lenses are to be manufactured from a glass of refractive
index 1.55, with both faces having the same radius of curvature. What is the
radius of curvature required if the focal length of the lens is to be 20 cm?
-
- A glass lens has a focal length of 5 cm in air. What will be its focal
length in water? Refractive index of glass is 1.51 and that of water is 1.33.
-
- A screen is placed 90 cm from an object. The image of the object on the
screen is formed by a convex lens at two different locations separated by 20
cm. Determine the focal length of the lens.
-
- For a given source of light, the angle of minimum deviation of a 600 prism
is 560. What is its refractive index?
-
-
-
- Calculate the angle of dispersion between red and violet colours produced
by a filter glass prism of refracting angle of 600.
-
- Calculate the dispersive power for crown and flint glass.
-
- Monochromatic light of wavelength 600 nm is incident from air to water.
What are the wavelength, frequency and speed of (i) reflected, and (ii)
refracted light. Refractive index of water is 1.33.
-
- In Young's double slit experiment, the two interfering sources are 0.5 nm
apart. Using l = 500 nm, interference fringes are
observed on a screen distant 1m. What is angular width of fringe?
-
- Sodium light l = 589 nm is incident on a Young's
double slit experiment. The separation between the two slits is 3.0 mm. If the
screen is placed at a distance of 4m from the slits, locate the position of
the tenth bright fringe on the screen.
-
- In Young's double slit experiment the slits are separated by 0.5 mm and
screen is placed 1.5 m away. The distance between the central bright fringe
and the fifth bright fringe is 1.5 cm. What is l?
-
- In a Young's experiment, the width of the fringes obtained with light of
wavelength 6000 nm is 2.0 mm. What will the fringe width be if the entire
apparatus is immersed in a liquid of refractive index of 1.33.
-
- Two coherent sources have intensities in the ratio of 81:1 what is the
ratio of maximum intensity to the minimum intensity in the fringe system?
-
- In Young's double slit experiment what is the intensity at a point on
screen where the two waves arrive at a phase difference of (i) 600
(ii) 900 and (iii) 1200?
-
- In Young's double slit experiment, the intensity at a point is 75% of
maximum intensity. What is the smallest distance of this point from the
central fringe? Given d = 0.1mm, D = 1m and l = 600
nm.
-
- A laser operates at 5 x 1014 Hz and has an aperture of 5 x 10-3.
What is the angular spread of the beam?
-
- Red light of l = 650 nm from a distant source falls on a slit of 0.5 mm
width. What is the distance between the two dark bands on each side of the
central bright band of diffraction pattern observed on screen placed 1.8 m
from the slit?
-
- What is the minimum aperture of the objective of a telescope, which will
enable two neighboring stars to be seen separately? The angle subtended by the
two stars at the objective of telescope is 3 x 10-6 radian. l= 546 nm.
-
- In Young's experiment, let the lights of l = 5.4 x
10-7 m and 6.85 x 10-8m be used in turn. Keeping the
same geometry, compare the fringe widths in the two cases.
-
- Two coherent sources of intensity ratio 100:1 interfere. Deduce the ratio
of intensity between the maxima and minima in the pattern.
-
- In Young's double slit experiment, we observe the 10th maximum
for l = 1000o A. What will be visible if the source of light is
replaced by light of wavelength 5000o A.
-
- The ratio of the intensities at minima to maxima in the interference
pattern is 9:25. What will the ratio of the widths of the two slits be in
Young's double slit experiment?
-
- In a star, hydrogen emits waves of l = 650 nm. The
"red-shift" in the wave length is 1.5 nm. What is the speed of the star with
respect to Earth?
-
- Two polarizing sheets are placed with their planes parallel so that light
intensity transmitted is maximum. Through what angle will either sheet be
turned so that intensity drops to half the maximum value?
-
- The critical angle of incidence of water for total internal reflection is
480 for a certain wavelength. What is the polarizing angle and the
angle of refraction for light on water at this angle?
-
- A glass plate (m= 1.5) is used as a polarizer.
Obtain the polarizing angle of incidence. What is the angle of refraction when
the reflected light is plane polarized?
-
- The spectral line for a given element in the light received from a distant
star is shifted towards a longer wavelength by 0.030%. Calculate the velocity
of the star in the line of sight.
-
- A diffraction grating one cm wide has 1000 lines and is used in the third
over. What are the diffraction angles for violet and orange lights? What is
the angular size of the diffraction maximum for monochromatic light? The
wavelengths for violet and orange are 400 nm and 600 nm respectively.
-
Let light travel from air to medium 1. If c and v1 are the
velocities of light in these media, the refractive index of medium 1 with
respect to air, or the absolute refractive index of medium 1.
Dual Nature of Radiation and Matter
When light of sufficiently small wavelength is incident on a metal surface,
electrons are ejected from the metal. This phenomenon is called as
'photoelectric effect' and the ejected electrons are called as 'photoelectrons'.
-
- When light of sufficiently small wavelength is incident on a metal
surface, electrons are ejected from the metal. This phenomenon is called as
'photoelectric effect' and the ejected electrons are called as
'photoelectrons'.
-
- According to wave theory when light falls on a metal surface, energy is
continuously distributed over the surface. All the free electrons receive
light energy and when the energy received exceeds that of work function, an
electron may escape the surface. If we user a low intensity source, it may
take hours before an electron to come out.s
-
- A photocell converts the change in the intensity of light into a change in
the electric current. The diagram shows a photocell circuit. The cathode is
made of photosensitive material.
-
- Photo voltaic cell converts light energy into electrical energy. It acts
as a cell. It consists of a metal layer of copper over which a semiconductor
layer of cuprous oxide coated with a thing film of silver or gold.
-
- The electrical resistance of a semiconductor depends on the intensity of
the incident light. A photoconductive cell works on the above principle.
-
- Photocells are used in television camera to reproduce sound recorded on
films, in counting devices, in burglar and fire alarms, to measure the
temperature of stars, to study the spectrum of heavy bodies, to operate street
light, to compare the illuminating powers of two sources, in photometers, for
locating minor flaws in metallic sheets, to determine the opacity of solids
and liquids, to control the temperature in chemical reactions and to determine
the Planck's constant.
-
- The suggestion that matter may have wave like properties was first put
forwarded in 1924-1925 by Louis De Broglie. He argued that if light, which
consists of waves according to classical picture, can sometimes behave like
particles, then it should be possible for matter, which consists of particles
to exhibit wave-like character under suitable circumstances.
-
- De-Broglie noted that according to the theory of relativity, the role
played by momentum 'P' and the energy 'E' of the particle is done by angular
frequency 'w' and the propagation vector 'k' of a
wave.
-
- Similar to the crystal diffraction patterns produced by X-rays, even the
beam of electrons of appropriate momentum could produce crystal diffraction
pattern.s
-
- The first experimental proof of the wave nature of electron was
demonstrated in 1927 by two American physicists C.J Davison and L.H Germer.
-
- In optical microscope, the ray of light can be bent by a lens system. By
placing the object and the lens system in such a way, we control the direction
of the ray to get a magnified image of the object.
-
- The phenomenon of interference, diffraction and polarization can be
explained by the wave theory of light.
Atoms and Nuclei
In the nineteenth century scientists saw enough evidence to prove that each
element has its distinctive atom. But all tem atoms contain identical electrons.
In spite of the fact that electrons carry negative charge, atoms as whole were
found to be neutral.
In the nineteenth century scientists saw enough evidence to prove that each
element has its distinctive atom. But all tem atoms contain identical electrons.
In spite of the fact that electrons carry negative charge, atoms as whole were
found to be neutral.
According to this model, an atom can be considered as a sphere of uniformly
distributed positive charge in which there are electrons distributed
symmetrically.
A radioactive source S emitting a particles was
collimated into a fine beam and made to fall on a thin gold foil. The a particles scattered in all directions.
The electric potential energy of the alpha particle at the distance of
closest approach from the nucleus.
Every atom consists of a nucleus containing the entire +ve charge. The whole
mass of atom is concentrated at this core.
Niels Bohr suggested that the problem about hydrogen spectrum can be solved
if we can make some assumptions.
An electron revolving in a stationary orbit of an atom absorbs some energy
the electron may jump over to an orbit of higher energy. This process is called
excitation and the atom is said to be in the excited state. The energy absorbed
to move from one orbit to the other is called excitation potential.
One can understand atomic spectra if one knows the concept of atomic energy
levels. The movements of electrons from one level to another causes the spectra.
The work of a spectoscopicst is to find the energy levels of an atom from the
measured values of the wavelengths of the spectral lines emitted by the atoms.
To analyze the spectra emitted by the lighter atoms is easy and that by heavier
atoms is difficult.
Moseley had done experiments on the characteristic X-rays and this led to the
development of the concept of atomic number.
The number of protons or the number of electrons in an atom in its normal
state is called the atomic number and is denoted by Z. The nucleus of every
element contains Z protons and some number of neutrons.
When an atom jumps from a higher energy stated to a lower energy state it
emits light in the form of photons. In any source of light, the light that is
emitted is incoherent, i.e., different photons have different phases and
different wavelengths.
It is the central core of the atom where the entire +ve charge and mass is
concentrated.
The unit in which atomic and nuclear masses are measured is called atomic
mass unit (a.m.u).
These are the elements having same atomic number but different mass number.
They have the same atomic number because the number of protons inside their
nuclei remains the same. The difference in their mass number is due to the
difference in their number of neutrons.
Einstein derived a formula given the relation between mass and energy as E =
mc2.
An atomic nucleus is a stable structure. The nucleus is bound by very strong
short range forces called nuclear forces. Certain amount of work has to be done
to separate the nucleons to such a distance that there is no interaction. This
work done therefore measures binding energy of the nucleus.
Average binding energy per nucleon is the total binding energy divided by the
mass number of the nucleus.
Physicists have categorized all forces occurring in nature under
gravitational, electromagnetic, strong nuclear and weak nuclear forces.
It is a spontaneous emission or disintegration of an unstable nucleus
resulting in certain radiations. The elements exhibiting this phenomena are
called radioactive elements. e.g., radium, thorium, actinium, polonium etc.
The number of atoms disintegrated per second at any instant is directly
proportional to the number of radioactive atoms actually present in the sample
at that instant.
Neutrons are considered as the best projectile particles to hit the target
(uranium) nucleus. The uranium may absorb these neutrons and become 92U236which
later splits into two smaller nuclei. In addition two neutrons are released and
energy is also released. This process is called a Nuclear fission.
A nuclear reactor is an installation where a self-sustaining nuclear fission
takes place in a controlled manner and energy released is used for constructive
purposes.
Nuclear fusion is the phenomenon of fusing two or more lighter nuclei to form
a single heavy nucleus.
Dalton had postulated that matter is made up of atoms, which are indivisible.
Thomson was the first to suggest a structure for an atom. According to him, an
atom is a positively charged sphere of radius=10-10 m in which the
mass and the positive charge of the atom are uniformly distributed. Inside the
sphere, electrons carrying equal negative charge are embedded like seeds in a
watermelon. This model failed, as it could not explain the origin of spectral
series of hydrogen atom.
Rutherford's alpha particle scattering experiment explained the structure of
atom and the size of nucleus.
What is the distance of closest approach to the nucleus of an alpha particle
which undergoes scattering by 180o in the Gelger- Marsden experiment?
Determine the radius of the first orbit of the hydrogen atom. What would be
the velocity and frequency of the electron in the first orbit? Given: h = 6.62 x
10-34 Js, m = 9.1 x 10-31 kg, e = 1.6 x 10-19
C, k = 9 x 109 N m2 C-2.
Calculate the value of constant.
Calculate the ionisation potential for a lithium atom
The second member of Lyman series in hydrogen spectrum.
Using the Rydberg formula, calculate the wavelengths of the first four
spectral lines in the Balmer series of the hydrogen spectrum.
Calculate the packing fraction of a particle
A nucleus of UX1 has a half life of 24.1 days. How long a sample
of UX1 will take to change 90% of it to UX2?
The half life of radon is 3.8 days. Calculate how much radon will be left out
of 10.24 milligram after 19 days?
Determine the half life of a radioactive material.
If 200 MeV energy is released in the fission of a sample nucleus of 92U235,
how many fissions must occur per second to produce a power of 1 kW?
The half-life of 92U238
against alpha decay is 4.5 x 109 years. How many disintegrations per second
occur in 1 g of 92U238?
Semiconductor Devices
In the chapter on current electricity, we had learnt about the flow of
charges, conditions to produce the flow and how different materials respond to
an external electric field. We had seen how materials are classified as
conductors and insulators.
In the chapter on current electricity, we had learnt about the flow of
charges, conditions to produce the flow and how different materials respond to
an external electric field. We had seen how materials are classified as
conductors and insulators.
Atoms are clustered together and are overlapped in solids. Therefore, the
outermost valence atoms are overlapped.
The electrons in the valence band are not capable of gaining energy from
external electric field and hence do not contribute to the current. This band is
never empty but may be partially or completely with electrons.
The atoms in a crystal are strongly held by covalent bonds in space at
tetrahedral angles. On receiving energy, a covalent bond breaks and an electron
is free to move in crystal lattice. This electron leaves an empty space (shown
as an open circle) called a hole.
When the impurity atom is a trivalent atom say indium, boron or aluminium,
these atoms will replace the silicon atom as shown.
When the impurity atom is a pentavalent atom say arsenic, phosphorus, these
atoms will replace the silicon atom as shown below.
When a p-type semiconductor is brought into a close contact with n-type
semiconductor crystal, the resulting arrangement is a PN junction or junction
diode.
Rectifier is a device which is used for converting alternating
current/voltage into direct current /voltage.
Junction diodes are of many types and solar cells are one such. Its working
is based on production of potential difference by sunlight. In other words, it
is a junction diode that can convert light energy into electrical energy.
Photodiode is essentially a P-N junction which works on the basis of electric
conduction from light. When light falls on such diodes and if the wavelength of
the light is such that the energy of the photon is sufficient to break a valence
bond, a new hole - electron pairs are created.
LED are light emitting diodes. It works in just the opposite way a photo
diode works. Photodiodes receive light and hence conducts differently. But LEDs
emit light using electric current.
The symbol of zener diode is shown above. When we studied about the diode
characteristics, it was found that under reverse bias, there is a small amount
of current due to the drifting of the minority charge carriers.
It is a semiconductor device having two junctions and three terminals. The
two types of transistors are p-n-p transistor and n-p-n junction transistors.
For proper working of a transistor, emitter base junction should be forward
biased and CB junction should be reverse biased.
There are digital circuits which either allow a signal to pass through or
stop it. The circuits other wise called as gate allows the signal to pass only
when some logical condition are satisfied. Under such condition the circuits are
called logic gates. They are building blocks of any digital system.
Arithmetic operations such as addition, subtraction and complex operations
such as multiplication, division etc., are performed by using digital circuits
called adders, which again consists of basic logical gates.
Energy band of a solid is the large number of energy levels confined in a
small region of energy range of a given solid, constitute what is known as
energy bands.
The two energy bands in solids are valence band and the conduction band.
Depending on the gap between the two bands, solids are classified as conductors,
insulators and semiconductors.
In an intrinsic semiconductor, the energy gap Eg is 1 eV. Its hole
mobility is very much smaller than electron mobility and is independent of
temperature. What is the ratio between conductivity at 600 K and that at 300 K?
Predict the effect on the electrical properties of a silicon crystal at room
temperature (300 K) if every millionth silicon atom is replaced by an atom of
indium.
A transistor is connected in common emitter configuration. The collector
supply is 8 V and the voltage drop across a resistor of 800 W
in the collector circuit is 0.5 V. If the current gain factor (a)
is 0.96, calculate the base current.
Communication Systems
The concept of information is central to communication. There is no precise
definition of the word "information". So, instead of information, we deal with
"message".
The concept of information is central to communication. There is no precise
definition of the word "information". So, instead of information, we deal with
"message".
The input transducer converts the message to an electrical signal say a
voltage or current. Another transducer at the destination converts the output
signal to the desired message form.
The above figure depicts the elements of a communication system. There are
three essential parts of any communication system, the transmitter, transmission
channel, and receiver.
A common format for encoding different kinds of message signals (e.g., speech
signal, video signal, computer data, etc.) for the purpose of transmission.
Attenuation is undesirable because it reduces signal strength at the
receiver. More serious, however, is distortion interference, and noise, which
appear as alternations of the signal shape. Although such contaminations may
occur at any point, the standard convention is to blame them entirely on the
channel. The transmitter and receiver are always treated as ideal.
In earlier times, the most widely used form of communication was a system
based on the transmission of a continuous-wave (CW) signal. With this system,
the signal was interrupted periodically (Morse code) to produce a coded message.
The velocity of electromagnetic waves is 3 x 108ms-1.
On the other hand, the velocity of sound waves cannot be used to transmit
intelligence to far off places. Only electromagnetic waves can be made to do
this.
In this type if modulation, wc and q are kept constant. The amplitude Ec of the
carrier wave is varied in accordance with the modulating wave.
When the amplitude of high frequency carrier wave is changed in accordance
with the intensity of the signal, it is called amplitude modulation.
The ratio of change of amplitude of carrier wave to the amplitude of normal
carrier wave is called the modulation factor m.
In amplitude modulation, the sidebands contain the signal. The power in the
sidebands is the only useful power. The power carrier by the side bands is only
33.3% even when there is 100% modulation. If modulation is 50%, then power
carried by the sidebands is 11.1%. Clearly, the useful power is small. So, the
amplitude modulation has low efficiency.
In frequency modulation, the frequency of the carrier wave is modified in
accordance with the amplitude of the modulating wave.
Various electrical machines and noises cause amplitude disturbance in the
transmission of amplitude-modulated wave. This makes the reception noisy.
In amplitude modulation and frequency modulation, the modulation was done by
sinusoidal signals. In pulse modulation, short pulses may do the modulation of a
radio-frequency carrier. The simplest of these is the conventional telegraph,
whereby information is transmitted by a code of dots and dashes, or by turning
the carrier on and off.
Demodulation is the process of recovering the signal intelligence from a
modulated carrier wave. This process, also called detection, is the reverse
process of modulation.
Telefacsimile's or Fax machines are a must for many businesses around the
world. The fax machine however, did not become widely used until the late
1980's.
The essential parts of a fax system are the transmitting devices that
translate the graphic material into electrical impulses according to a set
pattern, and a synchronized receiving device that retranslates these impulses
and prints that.
The 'modem' is a contraction of the term modulator-demodulator. It is a
conversion that facilitates the transmission and reception of the data over the
public switched telephone network (PSTN).
The simplest approach to the design of modems is to treat the entire PSTN as
a linear analog network. [Note that PSTN is almost entirely due to the use of
pulse-code modulation (PCM) for the transmission of voice signals.
A modem (a modulator/demodulator) lets you connect your computer to a
standard telephone line so that you can transmit and receive electronically
transmitted data.
Depending upon how your computer is configured and your preferences, you can
have an external, internal or PC modem card. All three types work the same way,
but each has its advantages and disadvantages.
When a modem first makes a connection, you will hear screeching sounds coming
from the modem. These are digital signals coming from the computer to which you
are connecting being modulated into audible sounds. The modem sends a
higher-pitched tone to represent the digit 1 and a lower-pitched tone to
represent the digit 0.
A computer performs its tasks by turning on and off a series of electronic
switches represented by the numerical digits of 0 and 1. A 0 is the code for
off, and a 1 is the code for on.
In an Earth environment, electromagnetic waves propagate in ways that depend
not only on their own properties but also on those of the environment itself.
Radio waves are electromagnetic waves of wavelength 10-3m and
higher. Their frequency range is from a few kHz to nearly a few hundred MHz.
As the wave is refracted, it is bent down gradually rather than sharply.
However, below the ionised layer, the incident and refracted rays follow paths
that are exactly the same as they would have been if reflection had taken place
from a surface located at a greater height, called the virtual height of this
layer.
Space waves travel in (more or less) straight lines. But they depend on
line-of-sight conditions. So, they are limited in their propagation by the
curvature of the Earth, except in very unusual circumstances.
Let us now discuss the basic principles of wireless radio communications. We
shall mainly concentrate on the principle of amplitude modulation and
demodulation.
The 'radar' beams microwaves towards a distant object and receives the
reflected signals. Since both the outgoing and incoming waves travel with the
velocity of light therefore by measuring the 'time delay' in receiving the
signal back, we can measure the distance of the object from the radar. In this
way, the precise location of the distant object is made possible.
Celestial bodies revolving around a planet are called satellites. Moon is a
natural satellite of the planet Earth. These days, the term satellite is used
for manmade satellites, which revolve around the Earth. The closed path of a
satellite around the Earth is called its orbit.
It is mainly done through geostationary satellites. These satellites are
fitted with special devices. These devices can receive signals from an Earth
station and transmit them again in different directions. These special devices
are called transponders.
"Remote Sensing" can be defined as obtaining information about an object by
observing it from a distance and without coming to actual contact with it.
Infact when we see an object and understand what it is, our eye is sensing that
object remotely. This is a broad definition. But we generally use this term for
observing the surface of Earth from space using satellites.
This type of wave propagation is said to be unguided. The uniform plane wave
exists throughout all space. The electromagnetic energy associated with the wave
spreads over a wide area.
A microphone is a device that transforms sound pressure into electrical
energy. In most types of microphone, the sound pressure acts upon a thin plate
or diaphragm, setting it into vibration, and this mechanical motion is then
utilised to produce electrical effects.
Two-way operation is essential for satisfactory telephone service, and many
of the problems of the industry arise from this fact.
The transmission lines used in telephony are of two kinds: open- wire and
cable. The open-wire lines are gradually being superseded by cable construction,
either overhead or underground, for two principal reasons.
An optical fiber is a dielectric wave guide that transports light signals
from one place to another just as a twisted-wire pair or a coaxial cable
transports electrical signals.
The laser is an acronym for Light Amplification by Stimulated Emission of
Radiation. The laser has been invented and developed in 1959 and 1960.
The below figure shows schematically how a population inversion can be
achieved so that laser action-or lasing us it is called can occur.
A laser beam departs from strict parallelism only because of diffraction
effects, determined by the wavelength and the diameter of the exit aperture.
Light from other sources can be made into an approximately parallel beam by a
lens or a mirror, but the beam divergence is much greater than for laser light.
The smallest lasers used for telephone communication over optical fibres have
as their active medium a semiconducting gallium arsenide crystal about the size
of a pin-head.
Ruby is a crystalline form of silica(Al2O3) with a
slight natural doping of chromium. It has the following advantages for being
used as a laser.
The glass discharge tube is filled with a 80%-20% mixture of the inert gases
helium and neon.
Let us consider the case of electromagnetic radiation in an ionised medium.
Suppose we increase/decrease the amplitude of an electromagnetic wave passing
through an ionised gas.