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

Explanation

When electric field E is applied on conductor force acting on free electrons
`{:(vec(F) = -evec(E)),(mvec(a) = -evec(E)):}`
`vec(a) = (-invec(E))/(m)`
Average thermal velocity of electron in conductor is zero
`(u_(t))_("av") = 0`
Average velocity of electron in conductors in `tau` (relaxation time) = `V_(d)` (drift velocity)
`V_(d) = (u_(t))_("av") + "a " tau`
`V_(d) = 0 + (-inEtau)/(m)`
`vec(V_(d)) = (-invec(E)tau)/(m)`