Derive the expression for the current density of a conductor in terms of the conductivity and applied electic field. Explain with reason how the mobility of electrons in a conductor changes when the potential difference applied is doubled, keeping the temperature of the conductor constant.

Explanation

From the relation `J=I//A " " I=" ne" Av_(d)`
Also`" " v_(d) = (eEr)/m rArr I= " ne"A((eEr)/m) = ("ne"^(2) A Er)/m`
or `I//A = ("ne"^(2)Er)/m =J " Here " p=m/("ne"^(2)r)`
So for current density J, conductivity `a=(1//p)`
we have `J=aE`
` Mobility " "mu=V_(d//E)=(er)/m`
As temperature is constant so relaxation time will be same and if we double the potential difference the mobility will change accordingly.