Question

A spherical conducting shell of radius $R$ has a charge q. A point charge $Q$ is placed at its centre. The electrostatic potential at a point P, distant $\frac{ R }{2}$ from the centre of the shell is :-

• A. $\frac{( q + Q )}{4 \pi \varepsilon_{0}} \frac{2}{ R }$
• B. $\frac{2 Q }{4 \pi \varepsilon_{0} R }$
• C. $\frac{2 Q}{4 \pi \varepsilon_{0} R }-\frac{2 q }{4 \pi \varepsilon_{0} R }$
• D. $\frac{2 Q}{4 \pi \varepsilon_{0} R }+\frac{ q }{4 \pi \varepsilon_{0} R }$

Answer 1

Answer: (D)

$V _{ p }=$ Potential due to $Q +$ Potential due to sphere
$V _{ p }=\frac{ kQ }{ R / 2}+\frac{ kq }{ R }$
$ \Rightarrow V _{ p }=\frac{ k }{ R }(2 Q + q )$