Question

Derive an expression for drift velocity of free electrons in a conductor.

Answer 1

Consider a conductor under the influence of electric field E. The force experienced by a free electron in a conductor is given by F = -eE, -ve sign shows that the divertion of F & E are in opposite direction.

∴ acceleration (a) = \(\frac{F}{m}\) = \(\frac{-eE}{m}\)

Since the average time elapsed between successive collision is called relaxation time (τ)

∴ Drift velocity (V_d) = 0 + aτ