Capacitor connected to an alternating voltage: Maxwell’s equations, Poynting’s theorem and oscillating L-C circuits

The behaviour of a parallel-plate capacitor connected to a sinusoidal alternating voltage is analysed and the electric and magnetic fields, as well as the electric and magnetic energies inside the capacitor are obtained. Aspects related to Maxwell’s equations, the Poynting vector and the conservation of electromagnetic energy are also discussed. Under certain conditions the electromagnetic energy stored in the capacitor remains constant and the behaviour of the capacitor at high frequencies is like that of an oscillating L-C circuit consisting of an inductor and a capacitor. The general situation is considered, valid for both low and high frequencies, and what is discussed here is of interest to students of an undergraduate electrodynamics course.