Dimensional Analysis and electric potential due to a uniformly charged sheet

TL;DR

This paper uses dimensional analysis and superposition to derive the electric potential of a uniformly charged square sheet, providing exact solutions and extending the method to triangular sheets for potential calculation.

Contribution

It introduces a novel approach combining dimensional analysis and superposition to determine electric potential on square and triangular charged sheets, including exact solutions.

Findings

Exact electric potential at any point on the square sheet

Potential behavior near the sheet's center

Extension to triangular sheets for potential calculation

Abstract

Dimensional analysis, superposition principle, and continuity of electric potential are used to study electric potential of a uniformly charged square sheet at its plane. It is shown that knowing the electric potential on the diagonal and inside the square sheet is equivalent to knowing it everywhere on the plane of square sheet. Behavior of electric potential near the center of the square is obtained. Then exact solution for the electric potential at any point on the plane of the square sheet is obtained. This result is used to calculate the electric potential of a right triangular sheet on its plane which can be used to find electric potential at any point on the plane of any uniformly charged polygon sheet.