Problem 3.134

A system consists of two thin concentric metal shells of radii $R_{1}$ and $R_{2}$ with corresponding charges $q_{1}$ and $q_{2} .$ Find the selfenergy values $W_{1}$ and $W_{2}$ of each shell, the interaction energy of the shells $W_{12}$ , and the total electric energy of the system.

W=W_{1}+W_{2}+W_{12}=\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{q_{1}^{2}}{2 R_{1}}+\frac{q_{2}^{2}}{2 R_{2}}+\frac{q_{1} q_{2}}{R_{2}}\right)

Electric Capacitance, Energy of an Electric Field