question_answer

A thin spherical conducting shell of radius \[R\] has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point p a distance \[\frac{R}{2}\] from the centre of the shell is                                   [AIEEE 2003]

A)            \[\frac{(q+Q)}{4\pi {{\varepsilon }_{0}}}\frac{2}{R}\]

B)                                      \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}\]

C)            \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}-\frac{2q}{4\pi {{\varepsilon }_{0}}R}\]          

D)            \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}+\frac{q}{4\pi {{\varepsilon }_{0}}R}\]

Correct Answer: D

Solution :

                     Electric potential at P                    \[V=\frac{k.Q}{R/2}+\frac{k.q}{R}\]                        \[=\frac{2Q}{4\pi {{\varepsilon }_{0}}R}+\frac{q}{4\pi {{\varepsilon }_{0}}R}\]