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Three identical parallel conducting plates A, B and C are arranged in order with B in the middle. Switches S1 and S2, when closed, connect A and C respectively to earth; both are initially open. A charge +Q is given to plate B. Which statement is correct?

1. If S1 and S2 are closed together, a charge Q/2 passes through each of S1 and S2.
2. If S1 is closed with S2 open, a charge Q passes through S1.
3. If S2 is closed with S1 open, a charge Q passes through S2.
4. All the above statements are incorrect.
5. If S1 and S2 are closed together, charge Q/3 passes through S1 and 2Q/3 through S2.

Correct answer: If S1 and S2 are closed together, a charge Q/2 passes through each of S1 and S2.

Solution

With B equidistant between identical earthed plates A and C, the charge +Q on B splits equally onto its two faces, inducing -Q/2 on each grounded outer plate. Hence Q/2 flows through each switch.

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