Derive the relationship between current in conductor and drift velocityin terms of number of free electrons per unit volume of conductor.

Therefore, the volume of the conductor = Al

If n is the number of free electrons per unit volume of the conductor, then the total number of free electrons in the conductor=A/n.

If e is the charge on each electron then total charge on all the free electrons in the conductor

Q=A/ne                                     (1)

Let a constant potential differences V is applied across the ends of the conductor with the help of a battery

The electric field set up across the conductor is given by

E=V/l

Due to this field, the free electrons present in the conductor will begin to move with a drift velocity vdtowards the left hand side of the conductor.

Thus the time taken by the free electrons to cross the conductor is

t=l/vd (2)

As current I=q/t                                                     (3)

By substituting equation (1) and (2) in equation (3),

We get

I=Alne/l/vd

Or                                      I=Anevd (4)

Since A,n and e are constant

I∞vd

Hence the current flowing through a conductor is directly proportional to the drift velocity.