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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[q2Rq2R+q2Rq3R+2q+q3R]=0

Solving this equation, we get

q=43q

2q+q=2q43q=23q

Therefore, charges on different surfaces in tabular form are given below:



Hence, option (d) is the correct answer.

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