Question

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

Answer 1

When electric field E is applied on conductor force acting on free electrons 

vector F = - e vector E

m vector a = - e vector E

vector a = (- e vector E)/ m

Average thermal velocity of electron in conductor is zero 

 (u_t)_av = 0 

Average velocity of electron in conductors in τ (relaxation time) = v_d (drift velocity) 

v_d = (u_t)_av + a τ 

v_d = 0 + (- e F.τ)/m

vector v_d = (- e F.τ)/m