A Modern Approach to Quantum Mechanics · Problem 14.1

Photons and Atoms — John S. Townsend

Physics — Quantum Mechanics · electromagnetic-field-energy-momentum

Problem

Show that the electromagnetic field energy is given by

H_{\text{E\&M}} = \frac{1}{8\pi}\int d^3r\,(\mathbf{E}^2 + \mathbf{B}^2)

and that the Poynting vector

\mathbf{S}_P = (c/4\pi)\mathbf{E}\times\mathbf{B}

gives the field energy per unit area per unit time.