Electromagnetism: Maxwell Equations, Wave Propagation and Emission

Chapter 10

Electromagnetic Waves

Maxwell’s equations couple the electric field E and the magnetic field B in a single physical entity, called the electromagnetic field. If one of the fields varies, necessarily, the other field is induced. Similar to the relation between displacement and pressure, which are responsible for the propagation of sound waves, the coupling between E and B is responsible for the propagation of electromagnetic waves in vacuum and in matter at the speed of light. It was not possible to foresee this remarkable effect before the formulation of Maxwell’s equations and electromagnetic theory. In 1884, Hertz confirmed the existence of these waves experimentally. He produced them by discharging two spheres at high potential mounted as an electric dipole. He verified that these waves propagate, interfere, diffract, and are polarized, exactly as light waves are. Today, we can produce electromagnetic waves of almost all frequencies from 10⁻² Hz to 10³² Hz. They play a fundamental part in telecommunications (radio, television, radar, etc.), in medicine (X-rays, gamma rays, laser), in industry, etc.

Electromagnetic waves are emitted by variable currents in the emitters and they are detected by receivers, in which they induce currents. They are specified by the fields E, D, B and H. They may be polarized and they carry energy, momentum, and other physical quantities. Their propagation properties depend on the medium.

In this chapter, after a brief mathematical review ...