Question

Using the concept of free electrons in a conductor, derive the expression for

the conductivity of a wire in terms of number density and relaxation time.

Hence obtain the relation between current density and applied electric field E.​

Answer 1

Answer:

Consider a conductor of length L and cross sectional area A , when potental difference v is applied across its end the current produced is i. If n is the number of electrons per unit volume in conductor and Vd is the drift velocity then,

I = -nAeVd Eq 1.

Where e is charge on electron , n is no of density.

Electric field produced at each point, E = V/L Eq 2.

if t is relaxation time and e is the electric field strength then drift velocity.

Vd = -etE / m Eq 3.

Substituting value in equation 1:

I = - neA(-etE / m )

I = (n e2t / m ) AE Eq 4.

As e = V/L then,

I = n e2t A / m x V/L

Or

V/I = m/n e2t x L/A

From other law R = V/I = m/n e2t x L/A

Answer 2

Explanation:

Consider a conductor of length L and cross sectional area A , when potental difference v is applied across its end the current produced is i. If n is the number of electrons per unit volume in conductor and Vd is the drift velocity then, I = -nAeVd Equaltion 1.