Question

Three concentric conducting spherical shells A, B and C of radius $R$, $2R$ and $4R$ carry charges $Q$, $-2Q$ and $4Q$ respectively. Then the energy stored between shells B and C is

• A. $\frac{Q^2}{16\pi {\epsilon }_{0}R}$
• B. $\frac{Q^2}{8\pi {\epsilon }_{0}R}$
• C. $\frac{Q^2}{12\pi {\epsilon }_{0}R}$
• D. $\frac{Q^2}{32\pi {\epsilon }_{0}R}$

Answer 1

The correct option is D $\frac{Q^2}{32\pi {\epsilon }_{0}R}$

$C_{BC}=4\pi {\epsilon }_0\times \frac{4R\times 2R}{4R-2R}\Rightarrow C_{BC}=4\pi {\epsilon }_0\times 4R$


Energy $E=\frac{Q_{BC}^2}{2C_{BC}}=\frac{Q^2}{2\times 4\pi {\epsilon }_0\times 4R}$