Drift velocity is the average velocity, which is attained by any moving electron when an external electric field is applied to it. It is caused by the electrons when moved in one direction. The derivation of drift velocity can be done by applying newton’s second law of motion, where the force is directly proportional to the acceleration of the object.
Derivation of drift velocity
The average velocity gained by free electrons of a conductor is given by,
v = I/ nAq
Where v is the drift velocity of electrons
I, is the current flowing through the conductorÂ
A, the area of cross-section of the conductorÂ
q, the charge on an electron
n, the number of electrons
The SI unit can be given as, m/s and is measured in m² /(V.s)
Let’s assume we have an electric field E in the conductor.
The force due to the electric field is much more than the interaction between the electrons. But let us consider the charge of an electron to be (-e).
The force on the electron is equal to
F=−eEF =−eE
The acceleration of the electron can be given as,
a=Fm=−eEm
as,
m is the mass of the electron.
As the relaxation time is the average time between two consecutive collisions, let us consider that there is ‘n’ number of electrons in the conductor at any given time.
The relaxation time is given will be ,
=Ï„ 1 +Ï„ 2 +Ï„ 3 +Ï„ 4 + ….nÏ„ =
Where, [Ï„1,Ï„2,Ï„3,Ï„4,..] are the collision time of n electrons
Then,
v d =v 1 +v 2 + v 3 + v 4 + v 5 …./ n
Applying the general kinematics equation,
v=u+atv=u+at ……… (2)
Where, v is the final velocity,
U is the initial velocity,
a is the acceleration,
t is the time duration.
Using equation (2) we get,
vd = (- eE/m)T
The v d given above is the expression of drift velocity
