A proper integral for the electric field at the surface of a conducting sphere

Abstract

In a recent paper, I have shown that the electric field at the surface of a charged conducting sphere evaluates to half the field discontinuity across the surface of the sphere. This exact result has been found by solving an improper integral, which has been criticized by Assad in a very recent paper in this journal [6]. In this note, I present a simpler approach that yields a proper integral for that field. This integral also evaluates to exactly half the field discontinuity, contrarily to Assad's objections.

Keywords:
Electrostatic fields; Gauss's law; Conducting sphere