Question

Derive the expression for drift velocity of free electron in terms of relaxation time and electric field applied across a conductor

Answer 1

Answer:

V(d)= (eE/m) T

where T= Relaxation Time

e= Charge on e

E= Electric Field Intensity

m=mass of electron

Explanation:

Consider an electron inside a conductor being drifted by the Electric field "E'".

The force acting on that electron due to the field is given by

F=eE -------> I (F=qE)

also,

If the electron is accelerated by " a" due to the force "F" then;

by newton's second law

F=ma--------->2

Equating I and 2; We get

ma=eE

a=eE/m

but

a= v/t

so,

v(d)/T=eE/m

v(d)= (eE/m)T.

Answer 2

Answer:

When conductor is subjected to an electric field E, each electron experiences a force.

F=-eE

and acquires an acceleration

a = F/m = - eE/m ________ (1)

Here m = mass of election, e = charge, E = electric field.

The average time difference between two consecutive collisions is known as relaxation time of election.

_____________ (2)

As v=u + at (from equation of motion)

The drift velocity v is defined as

Explanation: