A spherical shell of radius $$R_{1}$$ with uniform charge $$q$$ is expanded to a radius $$R_{2}$$. Find the work performed by the electric forces in this process.
As the field is conservative total work done by the field force,
$$A_{fd} = U_{i} - U_{f} = \dfrac {1}{2} q (\varphi_{1} - \varphi_{2})$$
$$= \dfrac {1}{2} \dfrac {q^{2}}{4\pi \epsilon_{0}} \left [\dfrac {1}{R_{1}} - \dfrac {1}{R_{2}}]\right ] = \dfrac {q^{2}}{8\pi \epsilon_{0}} \left [\dfrac {1}{R_{1}} - \dfrac {1}{R_{2}}\right ]$$.