On the influence of uniform singularity distributions

TL;DR

This paper derives exact 3D potential and force expressions for uniform singularity distributions on finite rectangular surfaces, enabling precise capacitance calculations for plates and cubes, and confirming consistency with existing special-case solutions.

Contribution

It provides new exact formulas for potential and force due to uniform singularities on finite rectangles, improving accuracy in capacitance estimation.

Findings

Accurate capacitance estimates for a unit square plate and a unit cube.

Expressions are valid throughout the physical domain and align with existing special cases.

Enhanced understanding of potential and force distributions on finite rectangular surfaces.

Abstract

Exact expressions for three-dimensional potential and force yield due to uniform singularity distributed on a finite at rectangular surface have been presented. The expressions, valid throughout the physical domain, have been found to be consistent with other expressions available as special cases of the same problem. Very accurate estimates of the capacitance of a unit square plate and a unit cube have been made using them.