From electrostatic potentials to yet another triangle center

TL;DR

This paper investigates the point of maximum electrostatic potential within a triangle, deriving new relations and establishing it as a novel triangle center not listed in existing catalogs.

Contribution

It introduces a new triangle center based on electrostatic potential, with derived relations and properties distinguishing it from known centers.

Findings

Identifies the electrostatic potential maximum point as a new triangle center.

Derives synthetic and analytic relations for the location of this point.

Shows this center is distinct from previously known centers in the literature.

Abstract

We study the problem of finding a point of maximal electrostatic potential inside an arbitrary triangle with homogeneous surface charge distribution. In this article we derive several synthetic and analytic relations for its location in the plane. Moreover, this point satisfies the definition of a triangle center, different from any of previously discovered centers in Clark Kimberling's encyclopedia. Writing style is slightly informal as the paper is targeted to a wide audience.