Electrostatic interactions of charges and dipoles near a polarizable membrane

A variational method is used to determine the polarization charge density induced on the surfaces of a dielectric slab (a coarse-grained model of a membrane) by electric point charges and extended dipoles. The results are used to obtain analytic expressions for the polarization energy and the resulting forces acting on and between pairs of charges positioned in various geometries relative to the membrane. The polarization effects are shown to be substantial and often non-trivial on the nanometre scale, compared to direct Coulomb interactions.