Diffusion of an Alternating Magnetic Field into a Sharply Cornered Conductive Region

The skin-depth solution for the penetration of an alternating magnetic field into a conductor breaks down in the vicinity of sharp corners, yet it is precisely such regions which are important in the study of liquid metal flows. This paper considers the behaviour of an alternating or rotating potential field diffusing into a two-dimensional wedge of arbitrary angle. The problem is reduced to a pair of integral equations over the boundary of the wedge which are solved numerically. The variation of the field lines over a time period is shown and the implications of the locally large Lorentz force for the fluid flow are discussed.