GPS Satellite Surveying, 4th Edition

Appendix EElectromagnetic Field Generated by Arbitrary Sources, Magnetic Currents, Boundary Conditions, and Images

Consider a source represented by electric current density measured in amperes/square meter. This vector characterizes the electric current distributed in space and flowing through an imaginary unit surface area (Balanis (1989)). The Maxwell equations with the source given read as follows:

E.1

E.2

We assume time harmonic fields with fixed angular frequency . Medium is assumed to be free space.

In order to solve these equations, the electric vector potential is introduced by the relationships

E.3

E.4

The thus introduced vector potential satisfies the Helmholtz equation

E.5