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Question

# Figure shows three concentric thin spherical shells A, B and C of radii R,2R and 3R. The shell B is earthed and A and C are given charges q and 2q, respectively. Find the charges appearing on all the surfaces of A, B and C.

A
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B
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C
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D
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Solution

## The correct option is D Charge distribution on shells is as shown in the figure below Since, there is no charge present inside shell A. The whole charge q given to the shell A will appear on its outer surface. Charge on its inner surface will be zero. Moreover if a Gaussian surface is drawn on shell B, net charge enclosed by it should be zero. Therefore, charge on its inner surface will be −q. Now let q′ be the charge on its outer surface, then charge on the inner surface of C will be −q′ and on its outer surface will be, 2q−(−q′)=2q+q′ as total charge on C is 2q. Given that Shell B is earthed. Hence, its potential should be zero. i.e, VB=0 ⇒14πε0[q2R−q2R+q′2R−q′3R+2q+q′3R]=0 Solving this equation, we get q′=−43q ∴2q+q′=2q−43q=23q Therefore, charges on different surfaces in tabular form are given below: Hence, option (d) is the correct answer.

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