Duality transformation in a three dimensional conducting medium with two dimensional heterogeneity and an in-plane magnetic field

The classical duality transformation of two dimensional continuum conductors is extended to three dimensional conductors with a two dimensional heterogeneity. This is used to discuss the classical magnetotransport of a periodic array of parallel cylindrical inclusions, which are either perfect insulators or superconductors, embedded in a free electron conducting host. A detailed understanding of the local field and current distributions is thereby achieved, and closed form expressions are obtained for the strong field magnetoresistance in some important configurations.