A very large sphere having charge 100e (e is equal to the charge of electron) uniformly distributed on the surface is compressed slowly and uniformly till its radius reduces to 1 m. The work done by the electric forces in this process is: (in J)

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$10^{13} \times e^{2}$

$4.5 \times 10^{9} \times e^{2}$

$9 \times 10^{13} \times e^{2}$

$4.5 \times 10^{13} \times e^{2}$

answer is D.

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Detailed Solution

$\begin{array}{l} {work done = U}_{i} - U_{f} \\ U_{i} = 0 as sphere very large no electrostatic interaction \\ U_{f} = self energy of sphere = \frac{Q^{2}}{8 π ε_{0} R} = \frac{9 \times 10^{9} \times {(100 e)}^{2}}{2 (1)} = 4.5 \times 10^{13} \times e^{2} \end{array}$

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