(d) The electric current in a metal due to an applied field is due to drift of electrons in a
direction opposite to the direction of the field.
Q3. Explain/Define the terms: a) Thermal velocity b) Drift velocity c) Relaxation time
c) Mean free path d) Mean collision time
(a) Thermal velocity:
A conductor consists of large number of free electrons of about
1029electrons/m3. Due to thermal energy these electrons are
moving in between the ions with a speed of 106m/s and collide
with ion cores of the conductor. After each collision velocity of
the electron becomes zero. There after start moving in random
direction. Thus in the absence of applied electric field, there is a
kind of randomness in the motion of electrons. Though the free
electrons are in motion, the net flow of current is zero or does
not give rise to any current.
“The average velocity with which the free electrons move inside the conductor due to
thermal energy is called thermal velocity”.
b) Drift velocity (vd):
When an electric field is applied, an electric field is developed inside the conductor. As a
result potential difference is developed between the ends of a conductor. The electrons start
moving opposite to the field direction and collide with ion cores. After each collision velocity
of electrons become zero; and again they gain velocity in a fresh direction but always
opposite to the direction of applied electric field. Even though randomness exists; distance
travelled as well as time of collision between the successive collisions is different.
“The average velocity with which electrons move in a conductor under the
influence of applied electric field is called drift velocity”.
The expression for drift velocity.
Consider a conductor of length „L‟ is subjected to an electric field E. In the steady state,
conduction electrons are drifted opposite to the direction of applied electric field. If „m‟ is
the mass of an electron, „vd‟ drift velocity, „τ‟ is the mean collision time, and then resistance
force „Fr‟ offered to its motion is given by
If „e‟ is the charge on the electron, „E‟ is the electric field, then force experienced by electron
due to applied electric field is F = eE
In the steady state
F = Fr
The drift velocity is given by