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MHT CET 2021 (20 Sep, Shift 1) · Electric Flux & Gauss's Law

Electric Flux & Gauss's Law question from MHT CET 2021 (20 Sep, Shift 1)

Q89MHT CET 2021 · 20 SEP · SHIFT 1Medium

Electric Flux & Gauss's Law

A spherical conducting shell of inner radius 'r ${}_{1}$ ' and outer radius 'r ${}_{2}$ ' has a charge 'Q'. A charge $-$ q is placed at the centre of the shell. The surface charge density on the inner and outer surface of the shell will be

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Answer: (a)

Field inside the conductor is zero, so the inner surface carries $+q$ to cancel the central $-q$ .
Total shell charge is $Q$ , so the outer surface carries $Q - q$ .
$\sigma_{in} = \frac{q}{4\pi r_1^2}$ , $\sigma_{out} = \frac{Q - q}{4\pi r_2^2}$
So the answer is (a).

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