In a previous physics course you should have encountered the interesting notion that the electromagnetic field carries energy and momentum. If you have ever been sunburned, you have experimental confirmation of this fact! We are now in a position to explore this idea quantitatively. In physics, the notions of energy and momentum are of interest mainly because they are conserved quantities. We can uncover the energy and momentum quantities associated with the electromagnetic field by searching for conservation laws. As before, such conservation laws will appear embodied in a continuity equation. Thus we begin by investigating a continuity equation for energy and momentum. As was mentioned earlier, there are systematic methods to search for continuity equations associated with a system of differential equations such as the Maxwell equations, but we will not get into that. Instead, we simply write down the continuity equation associated to energy-momentum conservation.
electromagnetic energy, maxwell equation, energy density, chapter 19
Torre, Charles G., "19 Electromagnetic Energy" (2012). Foundations of Wave Phenomena. Book 4.