A conducting body $1$ has some initial charge $Q$, and its capacitance is $C$. There are two other conducting bodies, $2$ and $3$, having capacitances : $C_2 = 2C$ and $C_3 \rightarrow \infty$ . 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 $N$ times. Then, the charge on body $1$ at the end must be
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When we touched first time charge on first capacitor beacomes $\frac{Q}{3}$ and on second capacitor it becomes $\frac{2 Q}{3}$ But when $2 C$ is touched with $C \rightarrow \infty$ it becomes uncharged so after first operation.
$Q_{1}=\frac{Q}{3}$
after $I I^{n d}$ operation $Q_{2}=\frac{1}{3}\left(\frac{Q}{3}\right)=\frac{Q}{3^{2}}$
so after $N^{t h}$ operation $Q_{N}=\frac{Q}{3^{N}}$
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