A geometrical description of charge distribution on the disordered conductor surfaces

TL;DR

This paper challenges the traditional belief that charge density on conductors increases with surface curvature, providing a qualitative geometric analysis that questions and refines this rule.

Contribution

It offers a new geometric perspective on charge distribution, questioning the conventional rule-of-thumb about charge accumulation at high-curvature points.

Findings

Charge density does not necessarily increase with surface curvature.

Qualitative analysis shows the traditional rule may be oversimplified.

Different geometric shapes exhibit varied charge distribution patterns.

Abstract

This paper considers the distribution of charge over the surface of a conductor, and specifically the old rule-of-thumb that charge accumulates near sharp points and more generally in regions of high curvature. The discussion is almost entirely qualitative. Various conductors with different geometric shapes have been considered and the charge density on their points has been compared. Our discussion shows that the statement "surface charge density is higher at points with greater curvature" does not seem to be true and at least it can be modified. We have avoided unnecessary relationships as much as possible and tried to follow the discussion qualitatively.