Mechanical and Electromagnetic Vibrations and Waves

Chapter 6

Electromagnetic Waves

A remarkable property of Maxwell’s equations (that was not possible to foresee before the formulation of the electromagnetic theory) is that they have solutions representing electromagnetic waves propagating at the speed of light in matter and in vacuum. The existence of these waves was experimentally confirmed, in 1890 by Hertz, who succeeded in producing them and verifying that they have the same propagation, interference, diffraction and polarization properties as light waves. Thus, Maxwell theory has enabled us to understand the nature of light as electromagnetic waves with very short wavelengths. Actually, we can produce and detect electromagnetic waves of frequencies varying between 10⁻² Hz and 10³² Hz, that is, of wavelengths varying between 10¹⁰ m and 10⁻²⁴ m. They play a very important part in nearly all branches of physics and have a considerable impact on economic, social, political and intellectual life. In this chapter, we recall the principal results of the electromagnetic theory, namely Maxwell’s equations. We discuss their wave solution and some applications of electromagnetic waves.

6.1. Principal results of the electromagnetic theory

The basic concepts of the electromagnetic theory are the electric field E and the magnetic induction field B (also called magnetic field for short) defined by their action on a charge q of velocity v

In the presence of dielectrics, we also have to introduce the electric displacement (also called ...