Electrostatic potential of a rectangular uniformly charged plate: exact solution and limiting cases

Abstract

In this paper I derive the exact solution to the electrostatic potential of a rectangular uniformly charged plate with charge density, σ, along the symmetry axis passing through its center, at distance z. The analytical solution generalizes recently obtained formulae for the special case of a square plate. Moreover, given the generality of the solution I obtain a set of limiting and particular cases well-known in the literature, such as: (i) the finite square plate; (ii) an infinite charged sheet; (iii) a 1D finite charged rod; (iv) a 1D infinite charged rod; (v) a single charge at the origin. I also discuss possible benefits of using these results in the context of teaching electrostatics in university physics classes, in the form of challenging exercises to be worked out in groups, and as a helpful tool to emphasize the power of limits and approximations in physics.