Derive an expression for drift velocity of electrons in a conductor. Hence deduce ohm's law.

Explanation

Derivation of the expression for drift velocity
Deduction of Ohm's law
Let an electric field E be applied the conductor. Accelerationi of each electron is
`a=(eE)/m`
Velocity gained by the electron eE
`y=(eE)/m t`
let the conductor contain n electrons per unit volume. The average value of time t between their succesive collision, is the relaxation time Z.
Hence average drift velocity `v_(d)=(eE)/m Z`
The amount of charge, crossing area A in time A? is
`=n e Av_(d)Deltat=IZ`
Substituting the vaue of `v_(d)` we get
`IZ=n eA((eE)/m)^(tau)`
But `I=JA`, where J is the current density
`implies = ((n e^(2) tau)/m)`
This is ohms's law.