question_answer

A spherical conducting shell of inner radius  \[{{r}_{1}}\]and outer radius \[{{r}_{2}}\]has a charge Q. A charge -q is placed at the centre of the shell. The surface charge density on the inner and outer surfaces of the shell will be

A) \[\frac{q}{4\pi r_{2}^{1}}and\frac{Q}{4\pi r_{2}^{2}}\]                   

B)  \[\frac{-q}{4\pi r_{2}^{1}}and\frac{Q+q}{4\pi r_{2}^{2}}\]

C)  \[\frac{q}{4\pi r_{1}^{2}}and\frac{Q-q}{4\pi r_{2}^{2}}\]                             

D)  \[0\,and\,\frac{Q-q}{4\pi r_{2}^{2}}\]

Correct Answer: C

Solution :

                                  Surface charge density \[(\sigma )=\frac{Ch\arg e}{Surface\text{ }area}\] \[\therefore \]  \[{{\sigma }_{inner}}=\frac{-q}{4\pi r_{1}^{2}}\]                and        \[{{\sigma }_{outer}}=\frac{Q-q}{4\pi r_{2}^{2}}\]