A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. Find the amount of heat produced when switch is closed. $(T a k e, K = \frac{1}{4 π ε_{0}})$

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$\frac{K q^{2}}{6 a}$

$\frac{K q^{2}}{2 a}$

$\frac{K q^{2}}{4 a}$

$\frac{K q^{2}}{3 a}$

answer is C.

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Detailed Solution

$H e a t p r o d u c e d = U_{i} - U_{f} = (U_{1} + U_{2}) - U_{2} = U_{1}$

$H e a t p r o d u c e d = \frac{q^{2}}{2 C} = \frac{q^{2}}{2 [4 π ε_{0} {\frac{a \times 2 a}{2 a - a}}]} = \frac{K q^{2}}{4 a}$

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