Two concentric, hollow spherical shells of radii R and 2R having charges Q and 2Q are as shown. Find the total electric potential energy of arrangement.

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$\frac{5}{2} \frac{{KQ}^{2}}{R}$

$\frac{2 {KQ}^{2}}{R}$

$\frac{{KQ}^{2}}{R}$

$\frac{3 {KQ}^{2}}{R}$

answer is A.

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Detailed Solution

Self potential energy, $U_{self} = \frac{{KQ}^{2}}{2 R} + \frac{K {(2 Q)}^{2}}{2 (2 R)} = \frac{3}{2} \frac{{KQ}^{2}}{R}$
Interaction energy, $U_{int} = \frac{KQ (2 Q)}{2 R} = \frac{{KQ}^{2}}{R}$
Total potential energy, $U_{tot} = U_{self} + U_{int} = \frac{5}{2} \frac{{KQ}^{2}}{R}$

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