question_answer

A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the conducting sphere is now given a charge of \[-3Q,\] the new potential difference between the same two surfaces is

A) \[V\]                     

B)        \[2V\]                    

C) \[4V\]               

D)        \[-2V\]

Correct Answer: D

Solution :

[d] When sphere has charge Q. The potential difference between'1'and '2'. \[{{V}_{1}}-{{V}_{2}}=K\frac{Q}{{{r}_{1}}}-K\frac{Q}{{{r}_{2}}}=KQ\left[ \frac{{{r}_{2}}-{{r}_{1}}}{{{r}_{1}}{{r}_{2}}} \right]=V\] When the sphere is given charge \[-3Q,\] the net charge in the sphere is \[(Q-3Q=-2Q)\] Hence new potential difference                                \[{{V}_{1}}-{{V}_{2}}=K\frac{(-2Q)}{{{r}_{1}}}-K\frac{(-2Q)}{{{r}_{2}}}\] \[=-2KQ\,\left[ \frac{{{r}_{2}}-{{r}_{1}}}{{{r}_{1}}{{r}_{2}}} \right]=-2V\]