Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Induced Electrostatic Fields in the Presence of Conductors and Dielectrics: A Purely Laplace Equation-Based Treatment

Version 1 : Received: 6 August 2023 / Approved: 7 August 2023 / Online: 8 August 2023 (07:34:45 CEST)
Version 2 : Received: 19 February 2024 / Approved: 19 February 2024 / Online: 20 February 2024 (06:06:22 CET)

How to cite: Bjornsen, G. Induced Electrostatic Fields in the Presence of Conductors and Dielectrics: A Purely Laplace Equation-Based Treatment. Preprints 2023, 2023080515. https://doi.org/10.20944/preprints202308.0515.v2 Bjornsen, G. Induced Electrostatic Fields in the Presence of Conductors and Dielectrics: A Purely Laplace Equation-Based Treatment. Preprints 2023, 2023080515. https://doi.org/10.20944/preprints202308.0515.v2

Abstract

This article studies electrostatic fields and potentials in the presence of conductors and point charges under the framework of solving Laplace’s equation with specifi ed boundary conditions. The results demonstrate that many problems posed and solved in elementary electrostatics through various heuristics such as the method of images, can be more rigorously treated under the solution framework of Laplace’s equation.

Keywords

potential; field; uniqueness; Legendre polynomial

Subject

Physical Sciences, Mathematical Physics

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