Chapter 9

Maxwell’s Equations

In 1865, Maxwell unified electricity and magnetism in a single theory, called electromagnetism. The fields E and B cannot be considered as independent, as the variation of one in time requires the presence of the other. Thus, they constitute a single physical entity, called the electromagnetic field. This theory is verified by all its consequences, particularly the existence of electromagnetic waves that propagate in vacuum with the speed Image equal to the speed of light. The existence of these waves with the same properties of polarization and propagation as light waves was verified experimentally by Hertz in 1884. Electromagnetic theory also solved the old problem of the nature of light: it is an electromagnetic wave of a very short wavelength. The formulation of electromagnetism was a very important event in the history of science.

In this chapter, we write Maxwell’s equations and the equations of propagation for the fields and the potentials. We discuss the questions of energy and its transfer and the radiation pressure.

9.1. Fundamental laws of electromagnetism

If electric and magnetic phenomena vary in time, all the relevant quantities (fields, free charge density qv, conduction current density j, polarization P, magnetization M, etc.) may depend on time, and we expect that some of the basic equations that we have derived in previous chapters will ...

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