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. In metals such as copper or aluminium, some of the electrons are free to move within the conducting material. These free electrons move randomly in all directions with a speed of the order of 106 ms-1. But, the electrons do not escape from the material as they are attracted to the positive ions of the material. Since the motion of the electrons is random, there is no net flow in any direction and hence the current is zero.
When the same metal is in an electric field, the electrons are subjected to a steady force given by 
If the electrons were moving in vacuum, the steady force would cause a steady acceleration in the direction of� 
an the electrons speed would have gone up. But in a conductor, the electrons undergo frequent collisions with the ions of the material. Hence, the direction of the electrons undergoes a random change. See figure below, the net effect is that in addition to the random motion of the electrons, there is also a very slow net motion or drift of the electrons. This drift or flow with a constant velocity (in a direction opposite to 
) is called the drift velocity VD.
To find the relationship between current and drift velocity, consider a conductor of length l and area of cross-section A. If V is the potential difference across the ends of the conductor, then the strength of the electric field is
The acceleration acquired by each electron due to the electric field is
where 
is the coulomb's force experienced by each electron and m is the mass of the electron.
The drift velocity of the electrons is given by
where t, the relaxation time, is the average time that an electron spends between two collisions. It is of the order of 10-14 s.
Now the volume of the conductor is equal to Al and if n is the number of free electrons per unit volume, then, the total number of free electrons in the conductor will be equal to n Al.
Hence, the total charge q = - n Ale
The time taken by free electrons to cross the conductor is
where we have substituted for t and q.
For a given conductor, I a Vd
A small value of drift velocity 10-5m/sec produces a large amount of current, as there are a large number of free electrons in a conductor.
The drift velocity of the electrons Vd is (using E = V / l)
Also I = - neAVd
On substituting for Vd in the above expression we get,
or
From this, the resistance R can be identified as
where,
R : resistance of the conductor
m : mass of the electrons
l : length of the conductor
n : density of free electrons in the conductor
e : electronic charge
A : area of cross-section
t : relaxation time
From this, the relaxation time r for a metal can be estimated, using the observed values of r. For copper at room temperature, r = 1.7 x 102 mW m. The number density of electrons is ~ 8.5 x 1022 m-3 (using the density of copper). Substituting these, along with the known values of m and e, we get t = 2 x 10-7 s, which agrees with values obtained by other methods.
Sub Topics
Mobility
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In metals, the mobile charge carriers are the electrons, in an ionized gas, they are electrons and positive ions; in electrolytes, these are both positive and negative ions. In a semiconductor such as Ge or Si, conduction is partly duer to electrons and partly due to holes which are sites of missing electrons. Holes act as positive charges.
The mobility m is defined as the magnitude of the drift velocity per unit electric field, i.e.,
Mobility is positive for both electrons and holes.
The electrical conductivity of a superconductor can be expressed as
s = neme + pemh
Here, me, mh are electron and hole mobilities and n,p are electron and hole concentrations.
The S.I unit of mobility is m2 / Vs.
Mobilities of some materials, at room temperature, in cm2/vs
| Material | Electrons | Holes |
|---|
| Diamond | 1800 | 1200 |
| Silicon | 1350 | 480 |
| Germanium | 3600 | 1800 |
| InSb | 800 | 450 |
| GaAs | 8000 | 300 |
