Cálculo aproximado do potencial eletrostático de um disco circular e um disco elíptico, com distribuição de carga homogênea, utilizando matemática elementar

Abstract

This work proposes an approximate methodology for determining the electrostatic poten tial generated by uniformly charged circular and elliptical disks using exclusively elementary mathematical tools. In contrast to the classical approach, which is based on differential and integral calculus, the proposed method relies on the geometric discretization of the surface charge distribution into successive rings, the use of finite summations, and algebraic simplification techniques. Initially, the methodology is developed for a uniformly charged circular disk, demonstra ting its convergence to the classical solution for the electrostatic potential. The procedure is then generalized to elliptical disks through an appropriate parametrization of the geometry, allowing the derivation of approximate expressions that incorporate the effects of eccentricity. The results show excellent agreement with the expected physical behavior, indicating that the corrections due to eccentricity appear as second-order terms relative to the circular case. In addition to reproducing the known solutions with good accuracy, the proposed methodology demonstrates that problems traditionally solved using integral calculus can be treated through systematic discrete procedures while preserving mathematical consistency and physical interpretation. Therefore, the method provides an alternative approach to the study of electros tatics and a valuable educational resource for teaching continuous charge distributions using elementary mathematical tools.