Analytical solution for the electric field in a half space conductor due to alternating current injected at the surface
An analytical expression for the electric field in a half space conductor, due to alternating current injected at the surface, is derived. Assuming that the injected current flows in wires perpendicular to the surface of the test piece, the problem can be formulated in terms of a single, transverse magnetic, potential. Considering at first one wire, the cylindrical symmetry permits simplification of the calculation by use of the Hankel transform. The final result for a system with two current-carrying wires is obtained by superposition.
The following article appeared in Journal of Applied Physics 95, no. 1 (2004): 344–348 and may be found at http://dx.doi.org/10.1063/1.1630700.