In a metal Conductor, there are extremely large number of free electrons. These free electrons move randomly with a thermal speed of the order of 105 to 106 m/s at room temperature.Im any portion of the conductor, the flow of electrons is so oriented that the average thermal velocity of total number of free electrons in a conductor is zero.
That is
Uav = u1+u2+u3+u4+u5....u6 / n = 0
Where u1 , u2 , u3 , u4 ...... un are thermal velocities of free electrons and n is the total number of free electrons.
When an electric field is applied across the conductor , the free electrons accelerate in a direction opposite to the direction of the applied field. Due to this acceleration, the electrons gain extra velocity but for a short time because the accelerated electrons collide with the ions in the conductor and during this collision , the extra velocity gained is destroyed . Again , the electron is Accelerated and comes to rest after collisions with ions.
Therefore , the motion of electrons acquire a small velocity called drift velocity (vd) in the direction opposite to that of the applied electric field . The flow of electrons with drift velocity from one end to another end of the conductor constitutes an electric current.
Expression for Drift Velocity:
Drift velocity is defined as the average velocity with which free electrons in a conductor get drifted in a direction opposite to the direction of the applied electric field.
Consider a conductor under the influence of electric field E . The force experienced by a free electrons in the conductor placed in the electric field is given by :
F = -eE
Negative sign shows that the direction of F and E are opposite to each other.
The acceleration produced in the electron is given by .
a = F/m
a = -eE / m
This acceleration lasts for a short time and is interrupted ( i.e made zero ) , when the accelerated electrons collide with the vibrating ions of the conductor .
This small interval of time between two successive collisions between electrons and ion in the conductor is called relaxation time or Mean free time (t)
Therefore , the drift velocity is given by
vd = u + at
vd = 0 + (-eE/m)t
vd = (-eE/m)t
Note : The Drift Velocity is of the order of 10-4 m/s which is negligible as compared to the average electrons thermal velocity of 106 m/s at room temperature.