Modification of Coulomb's law in closed spaces

TL;DR

This paper derives a modified Coulomb's law applicable in closed two- and three-dimensional spaces, showing that total charge must be zero in such spaces and exploring implications for universe models.

Contribution

It introduces a new form of Coulomb's law for closed spaces and links charge neutrality to the universe's spatial topology.

Findings

Total charge in closed spaces must be zero.

Modified Coulomb's law differs from the classical form.

Charge neutrality relates to the universe's spatial closure.

Abstract

We obtain a modified version of Coulomb's law in two- and three-dimensional closed spaces. We demonstrate that in a closed space the total electric charge must be zero. We also discuss the relation between total charge neutrality of a isotropic and homogenous universe to whether or not its spatial sector is closed.