A point source in the presence of spherical material inhomogenity: Analysis of two approximate closed form solutions for electrical scalar potential

A brief review of derivation of two groups of approximate closed form expressions for the electrical scalar potential (ESP) Gree n functions that originates from the current of the point ground electrode (PGE) in the presence of a spherical ground inhomogenity, are presented in this paper. The PGE is fed by a very low frequency periodic current through a thin isolated conductor. One of approximate solutions is proposed in this paper. Known exact so- lutions that have parts in a form of infinite series sums are al so given in this paper. Here, the exact solution is solely reorganized in order to fa cilitate comparison to the closed form solutions, and to estimate the error introduced by the approximate solu- tions. Finally, error estimation is performed comparing th e results for the electrical scalar potential obtained applying the approximate expres sions and accurate calcula- tions. This is illustrated by numerous numerical experimen ts.