Magnetostatic image method for the confocally layered elliptic cylinder

The two-dimensional (2-D) magnetostatic field problem of a homogeneous permeable elliptic cylinder embedded in a confocal layer of another permeable medium and containing an axially directed line current is reformulated as a problem of finding an equivalent current distribution inside the cylinder. Using some integral identities for the potential modes, the image source is identified as a line current at the location of the original current plus a combination of a sheet current and a bilayer distribution of current located on the fundamental strip between the two foci. The expressions for the image currents are tested analytically and illustrated numerically, and their relevance in the study of the impact of the layer permeability to the magnetic shielding efficiency is discussed.