Eddy current power dissipation at sharp corners: an external impedance solution applied to a wedge with large ratio of internal to external magnetic permeabilities

Abstract

The corner constant, which serves to correct the internal impedance per unit length of a conductor, is calculated in closed form for the limit of large ratios of internal to external magnetic permeabilities for a right angle comer. The solution is accomplished by means of a generalization of a method used in the problem of water waves on a sloping beach. The corner constant is determined by an integration of the surface axial electric field and the perfectly conducting magnetic field. Expansions of the axial electric field are also given because of its utility in future papers. The correct behavior of the surface magnetic field near the edge is determined by using the constant limit of the axial electric field in an internal Green's theorem representation. Rotation of the surface fields to a complex radial coordinate is discussed.