Coulomb interaction revised in the presence of material with negative permittivity

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.