Two thin conducting shells of radii R and 3R | vedclass

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(D) Let $q$ be the charge attained by the inner shell after earthing.$1$. With switch $S$ open: The inner shell is neutral $(q=0)$. The potential of t

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(D) Let $q$ be the charge attained by the inner shell after earthing.$1$. With switch $S$ open: The inner shell is neutral $(q=0)$. The potential of the inner shell is due to the outer shell: $V_{	ext{in}} = kQ/(3R)$. The potential of the outer shell is also $V_{	ext{out}} = kQ/(3R)$. Thus,$V_{	ext{in}} = V_{	ext{out}}$. Option $A$ is correct.$2$. With switch $S$ closed: The inner shell is earthed,so its potential becomes zero $(V_{	ext{in}} = 0)$. Option $B$ is correct.$3$. Calculation of induced charge $q$: The potential at the surface of the inner shell is the sum of potentials due to the inner charge $q$ and the outer charge $Q$.$V_{	ext{in}} = \frac{kq}{R} + \frac{kQ}{3R} = 0$$\frac{kq}{R} = -\frac{kQ}{3R}$$q = -Q/3$. Option $C$ is correct.Since all statements are correct,the answer is $D$.

Two thin conducting shells of radii $R$ and $3R$ are shown in the figure. The outer shell carries a charge $+Q$ and the inner shell is neutral. The inner shell is earthed with the help of a switch $S$.

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