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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 :
$\frac{{7{Q^2}}}{{24\pi {\varepsilon _0}R}}$
$\frac{{5{Q^2}}}{{16\pi {\varepsilon _0}R}}$
$\frac{{5{Q^2}}}{{8\pi {\varepsilon _0}R}}$
None
Solution
Radius $=R$
inner radius $=2 R$
outer radius $=3 R$
charge $=+2 Q$ hollow sphere a total charge $=-Q$
The electrostatic potential energy of this system$=$
By indication, inner wall of hollow sphere is induced with share $-2 Q$ and its outer surface with charge.
Two conducting concentric, hollow sphere $A$ and $B$ have radii $a$ and $b$ respectively.
$V=\frac{1}{4 \pi \epsilon_{0}} \times \frac{Q}{R}$
when, it is given that,
$V^{1}=\frac{1}{4 \pi \epsilon_{0}} \frac{2 Q}{2 R}$
$V^{11}=\frac{1}{4 \pi \epsilon_{0}} \frac{Q}{3 R}$
$V=\frac{Q}{4 \pi \epsilon_{0}}\left(\frac{2 Q}{2 R}+\frac{Q}{3 R}\right)$
$=\frac{1}{4 \pi \epsilon_{0}} \frac{6 Q+2 Q}{6 R}$
$=\frac{7 Q^{2}}{24 \pi \epsilon_{0} R}$
