Quasi-images and surface geometry in cavity electrostatics

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Abstract
A unit point charge placed within a general cavity in a dielectric medium induces a surface polarization charge density which is determined by a linear inhomogeneous integral equation. As the point source approaches the cavity surface, the polarization charge density becomes dominated by spatially singular terms. The two most singular contributions are calculated in a mean-curvature approximation. These contributions provide an approximate symmetric integral representation for the cavity Poisson-Green function which is exact throughout a spherical cavity in a conducting medium. For a general cavity, the approximation can be improved through the introduction of ‘‘quasi-images.’’ Numerical results are given for a cavity shape which models the geometry of an enzyme with a large indented active site.