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Q.

A conducting body 1 has some initial charge Q, and its capacitance is C. There are two other conducting bodies, 2 and 3, having capacitance: C2 = 2C and C3 = ∞. Bodies 2 and 3 are initially uncharged. Body 2 is touched with body 1. Then, body 2 is removed from body 1 and touched with body 3, and then removed. This process is repeated for N times. If the charge on body 1 at the end is found to be QxN, find the value of x.

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answer is 3.

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Detailed Solution

Initial charge on 1 = Q when C1 and C2 are touched⇒Q1Q2=C2C=12⇒Q1=Q3, Q2=2Q3Now when C2 and C3 are touched ⇒Q2Q3=C2C3=2C∞=0⇒Q2=0Again when C1 and C2 are touchedQ2=2(Q/3)3⇒Q1=(Q/3)3=Q9Similarly, we can say after N times it becomes QN=Q3N
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