On the Dependence of Charge Density on Surface Curvature of an Isolated Conductor

TL;DR

This paper investigates how the surface curvature of an isolated conductor influences its charge density, reviews existing theories, resolves discrepancies, and aims to develop a general analytic formula for this relationship.

Contribution

It provides a comprehensive review of prior work, resolves conflicting theories, and advances towards a general analytic expression linking charge density and surface curvature.

Findings

Resolved discrepancies between two major theories.

Discussed the applicability and limitations of the proposed formula.

Laid groundwork for a general analytic relation between charge density and curvature.

Abstract

A study of the relation between the electrostatic charge density at a point on a conducting surface and the curvature of the surface (at that point) is presented. Two major scientific literature on this topic are reviewed and the apparent discrepancy between them is resolved. Hence, a step is taken towards obtaining a general analytic formula for relating the charge density with surface curvature of conductors. The merit of this formula and its limitations are discussed.