Granular electrostatics: Progress and outstanding questions
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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/r 2 law. Every physicist also studies classical mechanics, and learns that the problem of three or more bodies in a 1/r 2 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.
KeywordsParticle Charge European Physical Journal Special Topic Volcanic Plume Dielectrophoretic Force Sakurajima Volcano
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