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An analytical solution for the distribution of surface charge on a dielectric sphere due to the presence of an external point charge is presented. This solution describes how charge on the surface of the sphere is polarised in the electric field into regions of negative and positive charge. The polarisation effect (distribution of surface charge) generally varies with the separation between the sphere and the charge, and it is particularly significant at very short separations. Results obtained from the classical electrostatic model are in qualitative agreement with density functional theory calculations of charge separation in C60 and C240 fullerenes in the presence of an external point charge. This suggests that, from an electrostatic point of view, in the static electric field of external charges these molecules exhibit dielectric behaviour.

Surface-charge distribution on a dielectric sphere due to an external point charge: examples of C60 and C240 fullerenes