Question

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 at a distance $R/2$ from the centre of the shell is :

• A. $\frac{2Q}{4\pi {\epsilon }_{0}R}$
• B. $\frac{2Q}{4\pi {\epsilon }_{0}R}-\frac{2q}{4\pi {\epsilon }_{0}R}$
• C. $\frac{2Q}{4\pi {\epsilon }_{0}R}+\frac{q}{4\pi {\epsilon }_{0}R}$
• D. $\frac{\left(q+Q\right)2}{4\pi {\epsilon }_{o}R}$

Answer 1

Answer: (C)

$\frac{2Q}{4\pi {\epsilon }_{0}R}+\frac{q}{4\pi {\epsilon }_{0}R}$

At P, potential due to shell :
$V_1=\frac{q}{4\pi {ϵ}_{0}R}$
At P , potential due to Q :
$V_2=\frac{Q}{4\pi {ϵ}_0\frac{R}{2}}$
$\therefore$ Net potential at P
$V=V_1+V_2$
$=\frac{q}{4\pi {ϵ}_{0}R}+\frac{2Q}{4\pi {ϵ}_{0}R}$