Question

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

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

Answer 1

Answer: (A)

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