Consolidated approach to two-body electromagnetic scattering

In this paper we present a new consolidated approach to the problem of determining the electromagnetic field resulting from a finite electric current source outside two electrically different media. This approach rests on properties of generalized functions and the solution of a given problem depends essentially only on the gradients of the characteristic functions of the various regions. In particular we study the scattered fields from a flat earth, from a two-layered earth, from an earth consisting of two different adjacent electrical media (the ``mixed-path'' problem), and from a rough surface. We show that each of these problems can be modeled and solved from one set of equations; in each case we carry the analysis to a stage where it agrees with that presented by the authors in specific detailed papers that treat each problem separately. As such the solutions can be shown to agree with classical approaches. The technique used here contains a minimum of sophisticated analysis and has the following properties: The source field is arbitrary, the resulting equations directly relate the unknown electric and known source field intensities without the use of intermediate Hertz potentials, and the boundary conditions evolve directly from the formulation as auxiliary equations.