Magnetic response of a hollow ellipsoid

The response of a ferrous ellipsoidal target in the presence of an applied magnetic field is studied. The ellipsoid is allowed to have two layers of contrasting magnetic permeability, and the frequency is assumed low enough to neglect any eddy currents. Because of its versatile geometry, the ellipsoid can represent several common shapes, such as discs, pancakes, cigars, and vertical or horizontal plates. Several special cases are considered in detail, including a hollow ellipsoid made of a thin, highly permeable shell. It is shown that the cross-polar component of the scattered field bears information about the ellipsoid's location.