Question

A metal ball of radius $R$ is placed concentrically inside a hollow metal sphere of inner radius $2R$ and outer radius $3R$. The ball is given a charge $+2Q$ and the hollow sphere a total charge $-Q$. The electrostatic potential energy of this system is:

• A. $\frac{7Q^2}{24\pi {ϵ}_{0}R}$
• B. $\frac{5Q^2}{16\pi {ϵ}_{0}R}$
• C. $\frac{5Q^2}{8\pi {ϵ}_{0}R}$
• D. $\frac{47}{120}\frac{Q^2}{\pi {ϵ}_{0}R}$

Answer 1

The correct option is A $\frac{7Q^2}{24\pi {ϵ}_{0}R}$

Radius $=R$

inner radius $=2R$

outer radius $=3R$

charge $=+2Q$

hollow sphere a total charge $=-Q$

The electrostatic potential energy of this system=

By indication, inner wall of hollow sphere is induced with share $-2Q$ and its outer surface with charge.

Two conducting concentric, hollow sphere $A$ and $B$ have radii $a$ and $b$ respectively.

$V=\frac{1}{4\pi {ϵ}_0}\times \frac{Q}{R}$

when, it is given that,

$V^1=\frac{1}{4\pi {ϵ}_0}\frac{2Q}{2R}$

$V^{11}=\frac{1}{4\pi {ϵ}_0}\frac{Q}{3R}$

$V=\frac{Q}{4\pi {ϵ}_0}(\frac{2Q}{2R}+\frac{Q}{3R})$

$=\frac{1}{4\pi {ϵ}_0}\frac{6Q+2Q}{6R}$

$=\frac{{7Q}^2}{24\pi {ϵ}_{0}R}$