Two conducting concentric hollow spheres have radii a and 2a. The inner shell has net charge Q on its surface. The outer shell is neutral. If the outer shell’s is connected to the earth the net heat generated is

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$\frac{1}{4 {πε}_{0}} \cdot \frac{Q^{2}}{4 a}$

$\frac{1}{4 {πϵ}_{0}} \cdot \frac{Q^{2}}{2 a}$

$\frac{1}{4 {πϵ}_{0}} \cdot \frac{Q^{2}}{a}$

Zero

answer is C.

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Detailed Solution

$H e a t G e n e r a t e d = U_{f} - U_{i}$

$U_{i} = U_{s e l f e n e r g y} = \frac{K Q^{2}}{2 a}$

after earthing, charge on outer sphere (inner side) will be -Q and on inner sphere (outer side) will be Q.

$\Rightarrow U_{f} = {U^{'}}_{s e l f e n e r g y} = \frac{K Q^{2}}{2 a} + \frac{K Q^{2}}{4 a}$

$\Rightarrow H e a t g e n e r a t e d = \frac{K Q^{2}}{4 a}$

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