and it can be seen that on the surface of the sphere (i.e. when r = R), the potential vanishes. The potential inside the sphere is thus given by the above expression for the potential of the two charges. This potential will not be valid outside the sphere, since the image charge does not actually exist, but is rather "standing in" for the surface charge densities induced on the sphere by the inner charge at p . The potential outside the grounded sphere will be determined only by the distribution of charge outside the sphere and will be independent of the charge distribution inside the sphere. If we assume for simplicity (without loss of generality) that the inner charge lies on the z-axis, then the induced charge density will be simply a function of the polar angle θ and is given by: