Granular electrostatics: Progress and outstanding questions

Every physicist studies electrostatics in the first year of graduate study, and learns that the electric field is a linear superposition of contributions from charges, each of which obeys a 1/r2 law. Every physicist also studies classical mechanics, and learns that the problem of three or more bodies in a 1/r2 field is intrinsically nonlinear. The contradiction between these two teachings is seldom commented upon. In this paper, I overview what is known, what is believed, and what remains entirely unknown about the behaviors of multiple electrically polarized or charged particles. I show that the nonlinearity recognized in classical mechanics leads to highly complex dynamics when particles are permitted to act in the presence of electric fields. I describe several simple problems that lead to effects that are not understood in any way, and I conclude with the proposition that what we know and believe are insignificant compared with the effects that we know to exist but cannot explain