A spherical capacitor composed of two concentric metal spheres one having a radius twice as large as the other. The region in which the energy is stored has a volume of

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$\frac{1}{4} \frac{c^{3}}{π^{2} ε_{0}^{3}}$

$\frac{3}{16} \frac{c^{3}}{π^{2} ε_{0}^{3}}$

$\frac{1}{384} \frac{c^{3}}{π^{2} ε_{0}^{3}}$

$\frac{7 C^{3}}{384 π^{2} ε_{0}^{3}}$

answer is D.

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Detailed Solution

$C = \frac{4 {πε}_{0} ab}{b - a}$

$\Rightarrow C = \frac{4 {πε}_{0} 2 a^{2}}{a}$

$\Rightarrow a = \frac{C}{8 {πε}_{0}}$

Volume in which field exists $= \frac{4}{3} {πb}^{3} - \frac{4}{3} {πa}^{3}$

$= \frac{7 C^{3}}{384 π^{2} ε_{0}^{3}}$

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