Gauss Theorem and Pointlike Charges: When Infinitesimals Make the Difference

Abstract

A classic application of the Gauss theorem is examined, showing how the choice of the Gaussian surface and the pointlike nature of the charge can determine results somehow unexpected for the student. Particular care must be paid not only to points where the field becomes infinite, but also to infinitesimal displacements of the charge and their direction. Pedagogical implications are outlined.