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A metallic spherical shell has an inner radius $R_{1}$ and outer radius $R_{2}$ . A charge is placed at the centre of the spherical cavity. The surface charge density on the inner surface is

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$= \frac{q}{4 π {R^{2}}_{1}}$

$= \frac{- q}{4 π {R^{2}}_{1}}$

$= \frac{q^{2}}{4 π {R^{2}}_{2}}$

$= \frac{q}{4 π {R^{2}}_{2}}$

answer is B.

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Detailed Solution

When a charge $+ q$ is placed at the centre of spherical cavity as shown in figure.

Charge induced on the inner surface of shell $= - q . . (i)$

Charge induced on the outer surface of shell $= + q . . (i i)$

$∴$ Surface charge density on the inner surface $= \frac{- q}{4 π {R^{2}}_{1}}$

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