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 $p$ a distance $\frac{R}{2}$ from the centre of the shell is

• A. $\frac{(q+Q)}{4\pi {\epsilon }_0}\frac{2}{R}$
• B. $\frac{2Q}{4\pi {\epsilon }_{0}R}$
• C. $\frac{2Q}{4\pi {\epsilon }_{0}R}-\frac{2q}{4\pi {\epsilon }_{0}R}$
• D. $\frac{2Q}{4\pi {\epsilon }_{0}R}+\frac{q}{4\pi {\epsilon }_{0}R}$

Answer 1

Answer: (D)

Electric potential at $P$,

$V=\frac{k\cdot Q}{R/2}+\frac{k\cdot q}{R}$
$=\frac{2Q}{4\pi {\epsilon }_{0}R}+\frac{q}{4\pi {\epsilon }_{0}R}$