Time-dependent fields and radiation

Abstract

Explicit time dependence occurs in Maxwell’s field equations in a way that can be said to describe processes of mutual induction of one field by changes in the other. The induction of electric field by a changing magnetic field is described by Faraday’s law of induction and the converse process by the displacement current. As the rates of change of the fields increase, these two processes increasingly assume equal importance and it becomes necessary to give equal consideration to both. When this is done, new features of the electromagnetic field are revealed: features that are completely missed in the quasistatic approximation where displacement current is neglected. The electromagnetic field no longer responds instantaneously to changes in its charge and current source. The response is delayed or retarded in time, with a retardation that increases with increasing distance from the source. There also arises a contribution to the total electromagnetic field that diminishes in magnitude with distance from its source less rapidly than static or quasistatic fields. This part of the total field, the radiation field, effectively becomes detached from its source to acquire, so to speak, a life of its own. The independence of electromagnetic radiation from its source is most strikingly demonstrated by its ability to exert appreciable physical influence on distant objects even long after the source has ceased to exist.