A conducting body 1 has some initial charge Q | vedclass

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Question

(A) When body $1$ (charge $Q$,capacitance $C$) is touched with body $2$ (charge $0$,capacitance $2C$),the total charge $Q$ is shared in the ratio of t

Vedclass · Accepted Answer

$Q/3^N$

Vedclass · Answer

(A) When body $1$ (charge $Q$,capacitance $C$) is touched with body $2$ (charge $0$,capacitance $2C$),the total charge $Q$ is shared in the ratio of their capacitances. The new charge on body $1$ is $Q_1' = Q 	imes \frac{C}{C + 2C} = \frac{Q}{3}$.After touching body $2$ with body $3$ (capacitance $C_3 ightarrow \infty$),body $2$ becomes uncharged because all its charge flows to the infinite reservoir of body $3$.Thus,after one complete operation,the charge on body $1$ becomes $Q_1 = \frac{Q}{3}$.After the second operation,the charge on body $1$ becomes $Q_2 = \frac{Q_1}{3} = \frac{Q}{3^2}$.Repeating this process $N$ times,the charge on body $1$ after $N$ operations will be $Q_N = \frac{Q}{3^N}$.

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