Three identical parallel conducting plates A, B, and C are placed as shown. Switches S1 and S2 are open, and can connect A and C to earth when closed . +Q charge is given to B.

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If S1 is closed with S2 open, a charge of amount Q will pass through S1.

If instead S2 were closed with S1 open, a charge of amount Q will pass through S2.

If S1 and S2 are closed together, a charge of amount Q/3 will pass through S1 and a charge of amount 2Q/3 will pass through S2.

If S1 and S2 are closed together, a charge of amount 2Q/3 will pass through S1, and a charge of amount Q/3 will pass through S2.

answer is A.

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Detailed Solution

When either A or C is earthed (but not both together), a parallel plate capacitor is formed with B with ±Q charges on the inner surfaces. (The other plate, which is not earthed, plays no role.) Hence, charge of amount +Q flows to the earth. When both are earthed together, A and C effectively become connected. The plates now form two capacitances in the ratio 1 : 2, and hence share charge Q in the same ratio.C1=ε0A2d,C2=ε0Ad⇒C1C2=12Now we can writeq1q2=C1C2=12because potential difference of both the capacitors is same and q1+q2=Q. Solving these, we get q1=Q/3,q2=2Q/3.

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