Question
Derive an expression for drift velocity of electrons in a conductor. Hence deduce Ohm's law.
Solution
Let an electric field E be applied the conductor. Acceleration of each electron is
Velocity gained by the electron
Let the conductor contain n electrons per unit volume. The average value of time't', between their successive collisions, is the relaxation time, 't'.
Hence average drift velocity 
The amount of charge, crossing area A, in time Δt is
=neAvdΔt = IΔt
Substituting the value of vd, we get
But I = JA, where J is the current density
