A spherical shell is uniformly charged by a charge q. A point charge $q_{0}$ is placed at its center. If the expansion of the shell is taking place such that its radius increases from $R_{1} to R_{2} (R_{2} > R_{1})$ then for this situation mark the correct statements

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The -work of electric forces in this process is $\frac{q (q_{0} + q / 2)}{4 π ϵ_{0}} [\frac{1}{R_{1}} - \frac{1}{R_{2}}]$

If external force is acting, then work done by external agent is -ve

If no external force is acting then energy would be released in this expansion

If no external force is acting then energy would be dissipated in this process

answer is A, B, D.

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Detailed Solution

$\begin{array}{l} U_{i} = \frac{q_{0}}{4 π ϵ_{0} R_{1}} \times q + \frac{q^{2}}{8 π ϵ_{0} R_{1}} \\ U_{f} = \frac{q q_{0}}{4 π ϵ_{0} R_{2}} + \frac{q^{2}}{8 π ϵ_{0} R_{2}} \\ \Rightarrow △ U = U_{f} - U_{i} = \frac{q (q_{0} + \frac{q}{2})}{4 π ϵ_{o}} [\frac{1}{R_{2}} - \frac{1}{R_{1}}] < 0 \end{array}$