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Image theory, previously developed for an electric low-frequency dipole in front of a dielectric sphere, is formulated for the magnetically permeable sphere. The low-frequency image source corresponding to an electric dipole outside the sphere arises only in the case when the orientation of the dipole is perpendicular to the radial direction. Two alternative image representations are developed. One is a combination of a magnetic strip current and a bifilar magnetic line current, both flowing between the center of the sphere and the Kelvin inversion point on the axis connecting the sphere and the dipole. The other is a combination of a magnetic strip current and an electric strip current flowing in orthogonal directions between the center and the inversion point of the sphere. A simple approximation for the image source is also derived.

In this work we have obtained the fields for external points created by uniformly magnetized ellipsoids and spheroids. The problem is solved directly in rectangular coordinates, obtaining the potential created by a uniformly charged ellipsoid everywhere by a variational method, in contrast to the usual method due to Dirichlet. Using the preceding result, we calculate the potential created by a uniformly magnetized ellipsoid in any external and internal points, as a superposition of the potentials created by two uniformly charged ellipsoids, which have opposite charge densities and slightly shifted centers. Finally, we find the solutions for the potential and field in any point external to a uniformly magnetized spheroid in rectangular coordinates. The results are checked with the classical ones obtained in spheroidal coordinates, finding a complete agreement except in one case. A discussion of this discrepancy is given. Finally, we determine how the magnetic field behaves with distance from the ellipsoid boundaries, which is very useful for corrections of the stray field flux and search coil design and also for models of particulate recording media with uniaxial anisotropy.

The asymptotic high-frequency solution for the scattered field produced by a plane wave incident on a perfectly conducting sphere coated with a thin composite material is considered. In the shadow region, the high-frequency scattered field is entirely associated with the usual creeping-wave diffraction. In the lit region, the scattered field can be expressed as a sum of geometrical optics (GO) and creeping-wave diffraction terms. The field in the caustic regions where the ray solution fails is excluded in this study. The appropriate formula for each term is derived and the result is presented in a form suitable for computation. Numerical results of the bistatic scattering patterns of the coated sphere show excellent agreement with the rigorous eigenfunction solutions.