Some applications of Maxwell’s equations in matter

This chapter comprises questions of a miscellaneous nature. They mostly have little in common except that all processes are time-dependent and occur within matter. The first few questions introduce some important preliminaries. For example, modifying Maxwell’s equations to include the effect of matter. The behaviour of the electromagnetic field at the boundary between two media having different properties is an important topic. The matching conditions (as they are known) are derived from both the integral and differential forms of Maxwell’s equations. Certain specific examples then follow, including some simple applications involving conductors, dielectrics and tenuous electronic plasmas. Along the way, the connection between Maxwell’s electrodynamics and the laws of geometrical optics is demonstrated explicitly.