Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 3 / 15D / a / Solution

In a region with no current, the Ampère-Maxwell equation and Faraday's law areThereforewhere the last line uses the divergence and curl of a cross product. Thus Poynting's theorem takes the formThe vector $\mathbf{S}$ is the Poynting vector.