Question

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

• A. $\frac{1}{4\pi {\epsilon }_0}\frac{Q}{6R}$
• B. 0
• C. $\frac{1}{4\pi {\epsilon }_0}\frac{2Q}{3R}$
• D. $\frac{1}{4\pi {\epsilon }_0}\frac{Q}{R}$

Answer 1

Answer: (A)

$q\to$ Charge appearing on shell of radius $2R$ after earthing
Calculating $q{V}_{\text{outer shell }}=\frac{KQ}{2R}+\frac{Kq}{2R}=0q=-Q$
Calculating potential at $r=\frac{3R}{2}$
$V_{\text{inner shell }}+V_{\text{outer shell }}=\frac{KQ}{r}+\frac{Kq}{2R}=\frac{KQ}{\frac{KR}{2}}+\frac{K(-Q)}{2R}=\frac{KQ}{6R}=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{6R}$