The potential difference applied across a given conductor is . . .

Question : The potential difference applied across a given conductor is doubled. How will this affect (i) the mobility of electrons and (ii) the current density in the conductor? Justify your answer.

Doubt by Pihu 

Solution : 

V'=2V (Given)

(i) Mobility (µ)
= Vd/E
=(eE𝞃/m)/E
=e𝞃/m
Clearly, mobility is independent of potential difference. Hence when the potential difference is doubled the mobility will remain same .i.e. there is no change in mobility. 

(ii) We know, current density is given by 
j=I/A

j=neVdA/A

j=neVd

j=ne(eE𝞃/m)
j=ne²(V/l)𝞃/m
j=ne²V𝞃/ml
Clearly 

j∝V

So when potential difference is doubled then current density will also get doubled.