All Problems

Electric Capacitance, Energy of an Electric Field

Problem 3.135

A charge \(q\) is distributed uniformly over the volume of a ball of radius \(R\). Assuming the permittivity to be equal to unity, find: (a) the electrostatic self-energy of the ball; (b) the ratio of the energy \(W_{1}\) stored in the ball to the energy \(W_{2}\) pervading the surrounding space.

Reveal Answer
(a) \(W=3 q^{2} / 20 \pi \varepsilon_{0} R\) (b) \(W_{1} / W_{2}=1 / 5\)