Propagation of waves on a wire above a lossy ground-different formulations with approximations

The characteristics of wave propagation guided by a single wire suspended in air above a lossy ground is studied with special regard to the distinction between the quantities: scalar potential, scalar potential to ground difference, and voltage to ground with their closed-form approximations of the correction terms. The propagation constant of the fundamental mode is addressed as is the difference in characteristic impedance depending on the formulation. The paper advocates the use of the magnetic vector potential together with the electric scalar potential and the complete solution for these in air and ground is given