Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 1 / 15D / d / Solution

The source-free equations imply $k\cdot E_0=0$, $\omega =c|k|$, andThereforeIt is parallel to $k$, and its period average isThe average electric and magnetic energy densities are equal:Hence $⟨u⟩={ϵ}_0|E_0{|}^2/2$ and $⟨S⟩=c⟨u⟩\hat{k}$, as summarized by energy density and flux of a plane electromagnetic wave.