Derive `sigma = (n e^(2) tau)/(m)`
where the symbols have their usual meaning.

Explanation

Consider a conductor of length l and area of cross section A. Let a p.d. of V be applied across its ends. Then drift velocity is
`v_(d)= a tau = (E e tau)/(m)` ….(1)
Current flowing through the conductor is `I= n Ae V_(d)` …(2)
`n rarr` number of free electrons per unit volume
`e rarr` charge on an electron,
Sub (1) in (2), i.e. `I= n Ae ((E e tau)/(m))= ((n A e^(2)tau)/(m)) E or (1)/(A)= ((n e^(2) tau)/(m)) E`.
`J= ((n e^(2) tau)/(m))E`
`therefore sigma E= ((n e^(2) tau)/(m)) E (therefore J= sigma E)`
`therefore sigma= ((n e^(2)tau)/(m))`