Consider two concentric conducting sphere of radii $\mathrm{R}$ and $2 \mathrm{R}$ respectively. The inner sphere is given a charge $+\mathrm{Q}$. The other sphere is grounded. The potential at $r=\frac{3 R}{2}$ is

• Correct answer
  A

  $\frac{1}{4 \pi \varepsilon_0} \frac{Q}{6 R}$
• B

  0
• C

  $\frac{1}{4 \pi \varepsilon_0} \frac{2 Q}{3 R}$
• D

  $\frac{1}{4 \pi \varepsilon_0} \frac{Q}{R}$

Solution

$q \rightarrow$ Charge appearing on shell of radius $2 R$ after earthing Calculating $\mathrm{q} \quad \mathrm{V}_{\text {outer shell }}=\frac{\mathrm{KQ}}{2 \mathrm{R}}+\frac{\mathrm{Kq}}{2 \mathrm{R}}=0 \quad \mathrm{q}=-\mathrm{Q}$ Calculating potential at $r=\frac{3 R}{2}$ $$ V_{\text {inner shell }}+V_{\text {outer shell }}=\frac{K Q}{r}+\frac{K q}{2 R}=\frac{K Q}{\frac{3 R}{2}}+\frac{K(-Q)}{2 R}=\frac{K Q}{6 R}=\frac{1}{4 \pi \varepsilon_0} \frac{Q}{6 R} $$

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