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Two metallic spheres of radii 1 cm and 2 cm are given charges $2\times10^{-5}\,\text{C}$ and $2\times10^{-4}\,\text{C}$ respectively. If they are connected by a conducting wire, the final charge on the smaller sphere is

1. $2\times10^{-3}\,\text{C}$
2. $2\times10^{-1}\,\text{C}$
3. $2\times10^{-4}\,\text{C}$
4. $2\times10^{-2}\,\text{C}$

Correct answer: $2\times10^{-2}\,\text{C}$

Solution

When connected by a wire, the two spheres come to the same potential, so $Q_1/R_1=Q_2/R_2$. With total charge conserved, the final charges divide in the ratio of radii, i.e. $1:2$. Hence the smaller sphere gets one-third of the total charge, which is $2\times10^{-2}\,\text{C}$.

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