Derive the expression for drift velocity of free electron in terms of relaxation time and electric field applied across a conductor.

Explanation

In the absence of electric field the electrons motion is random and the net velocity is zero. In the presence of electric field, they tend to flow opposite to that of the electric field in the conduction. If an electric field 'E' is applied across a length l of the conductor, the electrons will experirence an acceleration, `a = - (eE)/(m)`
If the average time for the acceleration is `tau`, the velocity required is
`vec(v)_(d) = vec(u) + vec(u) tau = vec(u) tau " " :. v_(d) = (e vec(E))/(m) tau, |vec(v)_(d)| (eE)/(m) tau`