General Laws of the Electromagnetic Field
Maxwell’s equations enclose the main experimental results on electricity and magnetism obtained in the late eighteenth and first half of the nineteenth-century by many scientists, in particular Coulomb, Volta, Ørsted, Ampère, Faraday, and Gauss.
The aim of this chapter is to return to these equations and to derive a series of consequences that are particularly relevant for the understanding of electromagnetic phenomena. Specifically, we will see how Maxwell’s equations imply the possibility to define two fundamental physical quantities for the electromagnetic field such as the energy density and the momentum density.
We will also see how the solution of Maxwell’s equations can be greatly simplified by the introduction of two potentials: the scalar potential and the vector potential, of which we will study the main properties. The last part of the chapter is dedicated to the study of plane electromagnetic waves, a particular solution of Maxwell’s equations in vacuum.