TITLE:
Dimensional Dependence of Electrostatic Equilibrium in Conductors: A Critical Analysis
AUTHORS:
Ektor G. Papanikos
KEYWORDS:
n-Dimensional Conductors, Charge Distribution, Potential Energy, Hyperspherical Coordinates, Gauss’s Law, Electrostatic Equilibrium, Dimensional Analysis
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.17 No.6,
June
30,
2025
ABSTRACT: The study examines the electrostatic charge distribution in n-dimensional conductors. By generalizing Gauss’s law and using hyperspherical coordinates, the ratio of electrostatic potential energies between a uniform distribution in the volume (WΘ) and a uniform distribution on the surface (WO) is calculated. For n ≤ 2, the two distributions are energetically equivalent, whereas for n > 2, the surface distribution is more favorable, with a ratio
W
Θ
/
W
O
=λ(
n
)=
2n/
(
n+2
)
. The main conclusion is that the concentration of charge on the surface constitutes an energetically favorable state only in spaces with more than two dimensions, revealing a fundamental difference in the behavior of electrostatic systems depending on spatial dimensionality. This study, providing new theoretical insight into the dimensional dependence of electrostatic equilibrium, could have applications in higher-dimensional theories.