Electrostatic Potential and It's Significance

 

Significance of Electrical Potential

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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. This concept is useful in calculations involving energies of charged particles. Not only that, as force is related to work, electric potential is closely related to the electric field 

Potential being a scalar quantity, it is easy to deal with, than electric field. Hence, when we need to determine an electric field, it is easy to find the potential first and find the field from it.

The electrostatic potential at any point in an electric field is defined as the work done in bringing a unit positive charge from infinity to that point against the electric force of the field.

V = W/q

where V is the potential

W is work done

q the charge

S.I. unit is Joule/Coulomb = 1 Volt

Potential Difference

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Consider two points in an electric field. If a free test charge +q_o was placed in the field, it would flow from b to a. So we say b is at higher potential. The electric field does negative work in moving the test charge q_o from a to b.

If a and b are two points in an electric field having a potential difference of 12V and if V_B>V_A, it means 12 Joules/C of work has to be done in moving a test charge from A to B. Conversely this 12 J/C of energy will be released if it moves from B to A. This process does not depend on the route traversed and like gravitational electrostatic forces are also conservative.

If a is at infinity, then the potential due to a single point charge

Electric potential at any point in vacuum due to group of point charges q₁,q₂,q_3……….q_n is equal to the algebraic sum of the potentials due to q₁,q₂,q_3……….q_n at point P. Algebraic sum is one in which, sign of the physical quantity is taken into account.

Problem:

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An infinite number of charges each equal to 'q' are placed along with X-axis at x = 1m, x = 2m, x = 4m, x = 8m, …………… and so on. Find the electric potential at the point x = 0 due to this set of charges.

Suggested answer:

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Step 1:

Potential is a scalar, hence no direction is involved.

Step 2:

The point where the potential is to be found is x = 0.

Step 3:

Which are the charges and where? All the charges are equal to 'q'. Position at 1m, x = 2m, x = 4m, x = 8m, ……………

Step 4:

The sign of all the charges is positive.

Step 5:

Step 6:

Using the superposition principle, net potential at

Step 7:

Need to simplify represents infinite geometric progression