Complementarity problems for two pairs of charged bodies

TL;DR

This paper models the electrostatic interaction between two charged bodies with stable charge distributions, analyzing the problem through complementarity conditions and focusing on the influence of charge distribution stability on interaction.

Contribution

It introduces a simplified model assuming stable charge distributions and classical electrical forces, providing a new framework for analyzing charged body interactions.

Findings

Formulation of the interaction as a complementarity problem.

Analysis of stable charge distributions under simplified conditions.

Insights into the influence of charge distribution stability on electrostatic forces.

Abstract

We consider an interaction of charged bodies under the following simplified conditions: the distribution of charge over each body is stable; the interaction of bodies is governed by electrical forces only. Physically, these assumptions can be treated as the following decomposition of charges: the structure of each body is assumed to be stable due to inner forces (say, quantum forces [1]), which do not influence the interaction of the bodies; the bodies interact due to the classical electrical forces [2] only. In this model, the role of inner forces is to create a specific stable distribution of the charge over a body. We assume that the charge distribution over a body can be described by the density of the charge. In our model, the distribution of the charge is the property of a body and does not change in the process of the bodies' interaction. For the simplicity we assume that the bodies are similar in the sense of geometry, say, occupy domain $Q$ and have a preferable direction of interaction denoted by $Ox_3$.