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Question

Figure shows two conducting thin concentric shells of radii r and 3r. The outer shell carries q while inner shell is neutral and is connected to earth by a switch S. Find the charge that will flow from earth to inner shell after the switch S is closed.



A
q2
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B
q3
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C
2q3
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D
q3
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Solution

The correct option is B q3
Let q be the charge on the inner shell when it is earthed (switch S is closed).

Since the shell is grounded , potential of inner shell, Vinner=0

Vinner=V1+V2

Where, V1 Potential due to outer shell on the inner shell.

V2 Potential due to charge present on the inner shell.

Vinner=14πεo[qr+q3r]=0

q=q3

Hence, option (a) is the correct answer.
Why this question: This question will check the basic understanding on application of concept of earthing.

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