Question

derive the expression for drift velocity in an electric field.

Answer 1

Let the electron have charge e, mass m and kept in a electric field E inside a conductor.

The force experienced by the electron F = eE

Acceleration due to the force = eE/m

Now displacement s due to the acceleration s = ½at²

Average velocity v_d (drift velocity = Total displacement / total time taken

= s/t

v_d = eE/2m