Eddy current power dissipation at sharp corners: asymptotic expansions of the field near and far from the edge of a right angle conducting wedge

Abstract

Asymptotic expansions are constructed for the fields both near the edge and far from the edge of a right angle conducting wedge. These expansions are needed for an accurate numerical solution of the problem to be carried out. Furthermore, previous results, such as a constant nonzero value of the axial electric field at the edge and linear-logarithmic behavior of the tangential surface magnetic field at the edge, are shown to be consistent with the rigorous expansions. Continuation of the expansions when the wedge angle is a rational multiple of pi is shown to involve logarithmic terms. Simpler expansions, when a complex rotation of the radial coordinate is performed, are also given.