ELECTROMAGNETIC POTENTIALS AND FIELDS OF SOURCES IN UNBOUNDED REGIONS

This chapter provides the electromagnetic (EM) fields of sources in unbounded, homogeneous media will be obtained directly without recourse to potential theory. Maxwell's equations, constitutive relations, and the equation of continuity, for a time harmonic variation of the source and fields in an isotropic medium are summarized for use in the development of electromagnetic potentials. The method of potentials allows one to construct the solutions to many EM field problems in a relatively convenient and systematic fashion. Helmholtz's theorem for vector fields states that any well‐behaved vector field can be represented in terms of its curl and divergence, respectively. Stated differently, such a vector field can be expressed as the sum of its solenoidal and irrotational parts. In the case of simple antenna and scattering geometries, the source distribution which produces the fields radiated by antennas, or scattered by obstacles, may be found in an approximate fashion as demonstrated in a few examples that follow.