that a dipole with dipole moment at vector position lying inside the sphere of radius R will have an image located at vector position (i.e. the same as for the simple charge) and will have a simple charge of: and a dipole moment of: Method of inversion The method of images for a sphere leads directly to the method of inversion. If we have a harmonic function of position where are the spherical coordinates of the position, then the image of this harmonic function in a sphere of radius R about the origin will be If the potential arises from a set of charges of magnitude at positions , then the image potential will be the result of a series of charges of magnitude at positions . It follows that if the potential arises from a charge density , then the image potential will be the result of a charge density . See also Kelvin transform Coulomb's law Divergence theorem Flux Gaussian surface Schwarz reflection principle Uniqueness theorem for Poisson's equation Image antenna Surface equivalence principle References Further reading Electromagnetism Electrostatics