Four concentric conducting shells $A, B, C$ and $D$ are arranged as shown in figure. A charge $+q$ is given to the outer most shell $D .$ Shell $B$ and $C$ are connected by conducting wire while Shell $A$ and $C$ is earthed. The equivalent capacitance of system is

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Aicharya · Accepted Answer

The outer shell of circle $D$ has $+q$ charge. Circle $A$ and $C$ has no charge in it due to earthing. So circle $B$ has $-q$ charge in it. We know that the capacitance between two concentric Circles of radius $r_1~\&~ r_2$ is $c=\frac{4 \pi \epsilon_0 r_1 r_2}{r_1-r_2}$ Here we take only $D$ and $B$ circle, as these two have charge in $t$. So the equivalent capacitance is $\begin{aligned} & c=\frac{4 \pi \epsilon_0 4 a \times 2 a}{4 a-2 a} \ & c=\frac{4 \pi \epsilon_0}{2 a} 2 a \times 4 a \ & c=16 \pi \epsilon_0 a \end{aligned}$ Therefore the equivalent capacitance of the system is $16 \pi \epsilon_0 a$. Option (B) is Correct. .

Four concentric conducting shells $A, B, C$ and $D$ are arranged as shown in figure. A charge $+q$ is given…

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