All Problems Electric Capacitance, Energy of an Electric Field
Problem 3.141
Each plate of a parallel-plate air capacitor has an area \(S\). What amount of work has to be performed to slowly increase the distance between the plates from \(x_{1}\) to \(x_{2}\) if (a) the capacitance of the capacitor, which is equal to \(q,\) or (b) the voltage across the capacitor, which is equal to \(V,\) is kept constant in the process?
3.141. (a) \(A=q^{2}\left(x_{2}-x_{1}\right) / 2 \varepsilon_{0} S\) (b) \(A=\varepsilon_{0} S V^{2}\left(x_{2}-x_{1}\right) / 2 x_{1} x_{2}\)