Question

Derive an expression for drift velocity of electrons in a conductor. Hence deduce Ohm's law. Also write the order of drift velocity.

Answer 1

Consider an electron of mass m and charge e moving inside a conductor with a drift velocity V_d  when an electric field E is applied. (E = V/l).

Force on electron = -Ee  

Acceleration of each electron = − Ee / m  

Mechanical force on electron = ma  

Velocity created due to this acceleration = Ee / m  τ  

where, τ is the time span between two consecutive collision. This ultimately becomes the drift velocity in steady state.

We know that current in the conductor i = neA V_d (n is no of free electrons in a conductor per unit volume)

This is as per Ohm's Law.