Question

Two concentric spherical shells are separated by vacuum. The inner shell has total change $Q$ and radius $r$. The outer shell has total charge $-Q$ and radius $2r$. The potential energy stored in the capacitor is

• A. $\frac{4Q^2}{7\pi {\epsilon }_{0}r}$
• B. $\frac{Q^2}{8\pi {\epsilon }_{0}r}$
• C. $\frac{Q^2}{2\pi {\epsilon }_{0}r}$
• D. $\frac{Q^2}{16\pi {\epsilon }_{0}r}$

Answer 1

The correct option is D $\frac{Q^2}{16\pi {\epsilon }_{0}r}$

Energy stored in a spherical capacitor is given by$$U=\frac{Q^2}{8\pi {\epsilon }_0}(\frac{1}{R_1}-\frac{1}{R_2})$$Substituting the data given in the question,

$U=\frac{Q^2}{8\pi {\epsilon }_0}(\frac{1}{r}-\frac{1}{2r})=\frac{Q^2}{16\pi {\epsilon }_{0}r}$

Hence, option (b) is the correct answer.

Why this question? This question is designed to test the basic understanding of spherical capacitor and energy stored in the capacitor.