Image theory for electrostatic and magnetostatic problems involving a material sphere

The well-known image method for a conducting sphere in front of an electrostatic source, due to Lord Kelvin from 1848, is generalized for electrostatic problems involving a dielectric sphere and for magnetostatic problems involving a permeable sphere. It is seen that the image sources are very simple, for a point source they consist of a point source plus a line source obeying a simple power law. The expressions are checked to satisfy all known limit cases. The image theory can be applied with simple computing devices for static or quasistatic problems involving material spheres.