All-space electrostatic potential of a uniformly charged finite rectangular plate

Abstract In this paper, we obtain the exact analytical solution for the electrostatic potential due to a uniformly charged, finite rectangular plate of dimensions 2 a × 2 b in all space. The result, expressed as a double sum, provides a simple and elegant generalization of a previous calculation by this author in Eur. J. Phys. 43 1 015203 (2022). Furthermore, it accurately reproduces the potential along the symmetry axis of the plate and its limiting cases. The novel solution also encompasses the special cases recently addressed by O. Ciftja and B. Ciftja in Can. J. Phys. 101 11 607–612 (2023), as well as their general solution, which is demonstrated to be equivalent to ours, obtained through direct integration and standard calculus techniques. We also discuss the pedagogical implications and potential uses of this result in university physics teaching, by stressing the importance of the uniqueness theorems in electrostatics.