The evolution of a mathematical description of the electric and magnetic force and induction phenomena associated with electric charges and currents is a fascinating chapter in the history of electromagnetic theory. Early "action at a distance" and later Faraday lines of force descriptions provided a pictorial vision of a "field" that Maxwell translated into a mathematical view of an electromagnetic field. Vector partial differential equations served to define space-time dependent electric and magnetic observables at every point in a field region. Although it is frequently customary to regard the Maxwell Equations as "God given", the following review attempts their derivation from physically intuitive experimental procedures.

Charges and currents (moving charges) are sources that excite time dependent force and induction phenomena at each point in the space surrounding these charges. A region of space-time, described by electric and magnetic observables that display the magnitude and direction of force and induction phenomena, is termed an electromagnetic field. Faraday visualized the field created by electric and magnetic charges in terms of lines of force that arise and end on these charges. Tensions along and pressures transverse to these lines, together with their motion, provided Faraday with a visual basis for describing various dynamical phenomena taking place in an electromagnetic field --but not completely. It remained for Maxwell, to symbolize mathematically the lines of force picture, and to complete the Faraday picture by adding the concept of an electric displacement current. This addition led to the identification of electromagnetic waves with light.

The following sections provide a brief review of the Electromagnetic field:

Introduction of observables that characterize the fields of electric and magnetic charges , i.e. static electric and magnetic fields.

The fields of electric and magnetic currents . and the concept of duality of currents.

Radiation and Force phenomena are summarized in the section on time-varying fields