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Q.

Two conducing concentric hollow spheres of radii a and 2a respectively are shown in the diagram. The inner shell has net charge Q on its surface. The outer shell is neutral. If the outer shell is connected to the earth the heat generated through the connecting wire is

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a

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

b

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

c

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

d

Zero

answer is C.

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Detailed Solution

$Heat Generated = U_{f} - U_{i}$

$U_{i} = U_{self energy} = \frac{{KQ}^{2}}{2 a}$

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

$\Rightarrow U_{f} = U_{self energy}^{'} = \frac{{KQ}^{2}}{2 a} + \frac{{KQ}^{2}}{4 a}$

$\Rightarrow Heat generated = \frac{{KQ}^{2}}{4 a}$

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Two conducing concentric hollow spheres of radii a and 2a respectively are shown in the diagram. The inner shell has net charge Q on its surface. The outer shell is neutral. If the outer shell is connected to the earth the heat generated through the connecting wire is