The apparent attraction between like-charged particles next to an oppositely charged planar surface

Abstract

The analytic solution of the Poisson equation for a system of two identical charges near a uniformly charged plane is used to understand the phenomenon of an attraction between a pair of charged particles next to an oppositely charged surface that has been observed recently. We found that there is no direct attractive interaction between like charges. We have shown that what is observed experimentally could be interpreted as the ‘apparent attraction’ resulting from the extra force experienced by each charge being in the non-zero plane parallel electric field due to the charged surface. This surface-induced electric field and force are directed to the center of the surface and can oppose the direct Coulomb repulsion between like charges. Both the field and force can be obtained naturally within the framework of classical electrodynamics if the effects of the finite size of a charged surface are taken into account.