Coulomb interaction revised in the presence of material with negative permittivity

TL;DR

This paper revises Coulomb's law in the context of materials with negative permittivity, revealing that electrostatic forces can switch from repulsive to attractive, leading to particle crystallization at equilibrium positions.

Contribution

It demonstrates how negative permittivity materials alter Coulomb interactions, using the method of images to show force reversal and particle crystallization.

Findings

Repulsive Coulomb force becomes attractive near negative permittivity materials.

Charged particles form stable equilibrium positions, or 'crystallize.'

Force reversal depends on the distance exceeding a critical value.

Abstract

Coulomb law is one of the fundamental laws in Physics. It describes the magnitude of the electrostatic force between two electric charges. Counterintuitively the repulsion force between two equal electric charges in a vacuum, stated by the Coulomb law, turn into the attraction force between the same electric charges when they are placed next to a material with negative permittivity and the distance between them is larger than some critical distance. As a result the equally charged particles "crystallize" occupying equilibrium positions. We prove this claim with the method of images for two charged particles placed next to a material with negative permittivity.