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$A, B$ and $C$ are three concentric metallic shells. Shell $A$ is the inner most and shell $C$ is the outermost. $A$ is given some charge and shell $C$ is earthed. Select the correct statement(s).

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The outer surface of $A, B$ and $C$ will have the same charge

The inner surfaces of $B$ and $C$ will have the same charge

The outer surface of $C$ will have no charge density

The inner surface of $B$ and $C$ will have same charge density

answer is A, D.

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Detailed Solution

The distribution of charges is shown in figure. We see that the inner surface of $B$ and $C$ possess the same charge $- Q .$ Also if $x$ is charge on outer surface of $C$ , then

$V_{C} = 0 \Rightarrow \frac{Q}{4 π ε_{0} c} + (\frac{- Q + Q}{4 π ε_{0} c}) + \frac{- Q + x}{4 π ε_{0} c} = 0 \Rightarrow x = 0$

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