Charge images in a dielectric sphere

The charge induced on the surface of a dielectric sphere by an external charge causes a field external to the sphere as if there were image charges inside the sphere and the material of the interior sphere were of the same dielectric constant as the material of the exterior. The images all lie on the radius containing the source charge. The image consists of a point charge at the inversion point together with a distributed charge along the line between the centre of the sphere and the inversion point. The field on the inside of the sphere is that produced by an image at the location of the source plus a line of distributed charge stretching out to infinity. Formulas are given for strength of the images for single and multiple source charges and for dipoles all for the full range of ratio of the dielectric constants of the interior of the sphere to its surroundings. Internal sources are also considered. The ponderomagnetic potential of the force on the sphere on the field of the source charge has a value equal to half of the electrostatic potential of the image in the field of the source