Basic equations for electromagnetic fields
Electromagnetic waves form a chapter of mathematical physics which can be organized as an axiomatic theory. Indeed, all the fundamental concepts, as well as many notions of technical interest, can be deduced from a small set of postulates. This chapter reviews the basic laws of slowly-varying electromagnetic fields. The mathematics of electromagnetism is drastically simplified in all those cases in which the constitutive relations are linear, i.e., when some, among those vectors, can be expressed as linear functions of the others. Among linear media, the simplest to describe and, at the same time, those of major practical interest, are isotropic media. The electromagnetic field which surrounds the wire “reacts” on the antenna, that is, it affects the distribution in the wire. A widely used approach consists of introducing auxiliary variables, which are usually referred to as scalar and vector electromagnetic potentials.