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Consider an assembly of three conducting concentric spherical shells of radii a, b and c as shown in figure. Find the capacitance of the assembly between the points A and B.

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$\frac{4 π \in_{0} ac}{c - a}$

$\frac{π \in_{0} ac}{c - a}$

$\frac{π \in_{0} ac}{c + a}$

$\frac{4 π \in_{0} ac}{c + a}$

answer is D.

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Detailed Solution

let a charge q is distributed on a Shell-I

$\begin{array}{l} V_{1} = \frac{1}{4 {πϵ}_{0}} (\frac{q}{a} - \frac{q}{c}); V_{2} \frac{1}{4 {πϵ}_{0}} (\frac{q}{b} - \frac{q}{c}) \\ V_{3} = 0; \end{array}$

$V_{1} - V_{3} = \frac{1}{4 {πε}_{0}} (\frac{q}{a} - \frac{q}{c});$

$C = \frac{q}{V_{1} - V_{3}}$

$\Rightarrow C = \frac{4 π ε_{0} ac}{c - a}$

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