Question

A point charge $Q$ is placed at the centre of a spherical cavity of radius $b$ carved inside a solid conducting sphere of radius $a$. Then total energy of the system is $\left[k=\frac{1}{4 \pi \varepsilon_{0}}\right]$

• A. $\frac{k Q^{2}}{2 a}-\frac{k Q^{2}}{2 b}$
• B. $\frac{k Q^{2}}{2 a}+\frac{k Q^{2}}{2 b}$
• C. $\frac{k Q^{2}}{a}+\frac{k Q^{2}}{b}$
• D. $\frac{k Q^{2}}{a}-\frac{k Q^{2}}{b}$

Answer 1

Answer: (A)

$-Q$ and $Q$ will be induced uniformly as shown.
Total energy $=$ Self-energy $+$ interaction energy

$= \frac{k(-Q)^{2}}{2 b}+\frac{k(Q)^{2}}{2 a}+\frac{k(Q)(-Q)}{b}+\frac{k(Q)(+Q)}{a}$
$+\frac{k(Q)(-Q)}{a}$
$=k Q^{2}\left(\frac{1}{2 a}-\frac{1}{2 b}\right)$