Question

A point charge Q is placed at the origin. Find the electrostatic energy stored outside the sphere of radius R centred at the origin.

Answer 1

Given:
Charge on the sphere = Q
Radius of the sphere = R
Capacitance of the sphere, $C=4\pi {\in }_{0}R$
Thus, the energy of the sphere is given by
$$\begin{gathered} E=\frac{1}{2}\mathrm{C}{V}^2 \\ =\frac{1}{2}\times 4\pi {\in }_{0}R\times \frac{Q^2}{{\left(4\pi {\in }_{0}R\right)}^2} \\ =\frac{Q^2}{8\pi {\in }_{0}R} \end{gathered}$$