A thin spherical conducting shell of radius $R$ is given a charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at the point $P$ at a distance $\frac{R}{2}$ from the centre of the shell is

• A

  $\frac{2Q}{4\pi {\epsilon }_{0}R}-\frac{2q}{4\pi {\epsilon }_{0}R}$
• Correct answer
  B

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

  $\frac{(q+Q)}{4\pi {\epsilon }_0}\frac{2}{R}$
• D

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

Solution

Potential due to point charge
$V_1=\frac{Q}{4\pi {\epsilon }_0\left(\frac{R}{2}\right)}$

Potential due to shell at inside point

$V_2=V_{\frac{R}{2}}=V_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}}$

$V_2=\frac{q}{4\pi {\epsilon }_{0}R }$

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

Hence, the correct answer is option: 'B'.