Discussion
The distance between the centres of two identical solid spheres each of radius 5 cm kept in free space is 40 cm. If each one is holding a charge of 2 μC, then the work done in bringing their centres to a separation of 30 cm is
Answer: E
The work done is \(3 \times 10^{-2}\) J.
Outside them, charged spheres act as point charges at their centres. The work equals the increase in potential energy.
\[ \begin{aligned} W &= kq^{2}\left(\frac{1}{0.3} - \frac{1}{0.4}\right) \\ &= 9 \times 10^{9} \times 4 \times 10^{-12} \times \frac{5}{6} \\ &= 0.036 \times \tfrac{5}{6} = 0.03\ \text{J} \end{aligned} \]
The radius of the spheres does not matter as long as they do not overlap. \(12 \times 10^{-2}\) J is the final energy \(\frac{kq^{2}}{0.3}\), not the change.
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