All Problems

Electric Capacitance, Energy of an Electric Field

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.

Reveal Answer
W=W1+W2+W12=14πε0(q122R1+q222R2+q1q2R2)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)
Prev
Next