Question

The three concentric conducting spherical shells of radii $R,2R$ and $3R$ carry charges $Q,-2Q$ and $3Q$ respectively. The total electrostatic energy stored in the system

• A. $\frac{Q^2}{10\pi {ϵ}_{0}R}$
• B. $\frac{Q^2}{4\pi {ϵ}_{0}R}$
• C. $\frac{Q^2}{\pi {ϵ}_{0}R}$
• D. $\frac{Q^2}{2\pi {ϵ}_{0}R}$

Answer 1

The correct option is B $\frac{Q^2}{4\pi {ϵ}_{0}R}$

The net electrostatic potential of the system,

$V_{\text{net}}=\frac{kQ}{R}-\frac{2kQ}{2R}+\frac{3kQ}{3R}=\frac{kQ}{R}$

Also, net charge of the system,

$q_{\text{net}}=Q+(-2Q)+3Q=2Q$

Now, potential energy of the system,

$U=\frac{1}{2}{q}_{\text{net}}{V}_{\text{net}}=\frac{1}{2}\left(2Q\right)\frac{kQ}{R}=\frac{k{Q}^2}{R}=\frac{Q^2}{4\pi {ϵ}_{o}R}$
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