A spherical conducting shell of inner radius $R_{1}$ and outer radius $R_{2}$ has charge $Q$ . Now a charge $q$ is placed inside the shell but not at centre, then surface charge densities with their nature on inner and outer surfaces of the shell are respectively,

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$\frac{- q}{4 π {R_{1}}^{2}} (u n i f o r m), \frac{Q + q}{4 π {R_{2}}^{2}} (n o n - u n i f o r m)$

$\frac{- q}{4 π {R_{1}}^{2}} (n o n - u n i f o r m), \frac{Q + q}{4 π {R_{2}}^{2}} (u n i f o r m)$

$\frac{q}{4 π {R_{1}}^{2}} (u n i f o r m), \frac{Q + q}{4 π {R_{2}}^{2}} (n o n - u n i f o r m)$

$\frac{- q}{4 π {R_{1}}^{2}} (n o n - u n i f o r m), \frac{Q}{4 π {R_{2}}^{2}} (u n i f o r m)$

answer is B.

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Detailed Solution

Due to induction -q , will induce on inner surface of shell Q .

As the total charge of shell is Q, so charge equilibrium condition in $Q + q$ will be on the outer surface of shell.

The charge distribution on inner surface of shell would be non- uniform , because electric field at any outside point $(r > R_{1})$ due to inside charges (q and -q) has to be zero which is possible only when -q is distributed non-uniformly.

Charge on outer surface would be uniform

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