Low-frequency image theory for a current dipole in front of a permeable sphere

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 Bowing in orthogonal directions between the center and the inversion point of the sphere. A simple approximation for the image source is also derived.<>