Abstract-Maxwell equations can be used to formulate an analytical full time-domain theory of skin effect phenomena in circular cylindrical conductors without any detour into the frequency domain. The paper shows how this can be done and concomitantly provides the means to determine the time-varying per unit length voltage drop along the conductor from a given time-varying conductor current. The developed relationship between voltage and current is not very complicated and led the authors to examine the reasons why it has never been utilized in transient analysis, nor given special emphasis in the literature. Those reasons are thoroughly examined and the conclusion is that the conditions required for the application of a purely time-domain skin effect theory are very restrictive.

In a time dependent solution of electromagnetic field penetration into a conductor, it turns out that the impedance power series solution diverges sharply if the ratio conductor radius to skin depth a/δ exceeds 2.7, close to the mathematical irrational number e. This problem has previously been considered to be due to the role of inversion. However, in this paper we show that the power series solution may be derived analytically from Bessel function solutions where the latter does not show the divergence problem. Experimental results are presented and we find that the logarithmic slope of the ac resistance and reactance change close to the value a/δ=e in both models. Since both models are based on the solution of a diffusion-like equation then the divergence effect at e may be expected to occur in other diffusion processes.