A point charge ‘Q’ is placed at the centre of a spherical cavity of radius ‘b’ created inside a solid conducting sphere of radius ‘a’. Then total electrostatic potential energy of the system is: $[k = \frac{1}{4 {πϵ}_{0}}]$

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$\frac{{kQ}^{2}}{2} [\frac{1}{a} - \frac{1}{b}]$

$\frac{{kQ}^{2}}{2} [\frac{1}{a} + \frac{1}{b}]$

$2 {kQ}^{2} [\frac{1}{a} + \frac{1}{b}]$

${kQ}^{2} [\frac{1}{a} + \frac{1}{b}]$

answer is A.

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Detailed Solution

U_total = Self energy + energy of interaction

$= \frac{k (- Q^{2})}{2 b} + \frac{{kQ}^{2}}{2 a} + k \frac{Q (- Q)}{b} + \frac{kQ \cdot Q}{a}$

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