The field equivalence principle: illustration of the establishment of the non-intuitive null fields

The field equivalence principle, one of the fundamental concepts in electromagnetics, has numerous applications. However, for a beginning student, it is not easy to understand this concept thoroughly and to appreciate it. The dilemma faced by beginning students is illustrated. We have sources in a finite Region I, and an arbitrary mathematical surface separating Regions I and II. The equivalent problems for the exterior and interior regions are specified with the use of electric and magnetic equivalent currents impressed on the boundary surface. The acceptance of the establishment by the equivalent sources of the non-intuitive null field for the exterior problem (by the equivalent sources and the original source for the interior problem) is commonly bothersome and not comfortably realized. In order to clarify this, we revisit Love´s and Schelkunoff s forms of the equivalence principle. Subsequently, we discuss two simple, analytically tractable illustrative examples, consisting of plane-wave fields in two half-space regions, separated by an infinite planar surface. In particular, the emphasis is on the establishment of the non-intuitive null fields developed by these equivalent sources. Various forms of equivalence are illustrated by simple analytical field expressions