Eddy current power dissipation at sharp corners: transmission lines and local partition of the internal impedance of conductors

Abstract

A general formula is derived, within the framework of the low frequency transmission line formulation, for the internal impedance per unit length of good conductors in terms of the surface electric field. This is used to partition the internal impedance per unit length into a part resulting from the perfectly conducting surface current distribution and corrections resulting from local surface features such as sharp corners. The two electrical properties, skin depth and surface impedance divided by the product of frequency times external magnetic permeability, must be small compared to other distances in the problem (for example the distance between local features such as corners) for this partitioning to be useful. The concept of how the sizes of these two electrical parameters and the ratio of internal-to-external magnetic permeabilities influence the use of approximations, such as the surface impedance approximation, is discussed and illustrated on the problem of a current filament above a conducting half space. The general results obtained in this paper are applied in future papers to obtain the local impedance corrections for right angle corners with arbitrary ratios of internal-to-external magnetic permeabilities.