2000/11/07 by Mario H. Oliveira, Mário H Oliveira, Jose A. Miranda +1 · 2 citations
Physics and Astronomy · #Magnetic properties of thin films #Quantum and Classical Electrodynamics #Theoretical and Computational Physics #physics.class-ph #physics.gen-ph
paper · pdf · doi:10.1088/0143-0807/22/1/304
14 pages, 6 figures, RevTex, accepted for publication in the European Journal of Physics
arxiv created 2000/11/07 · openalex publication_date 2001/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The Biot-Savart law is a well-known and powerful theoretical tool used to calculate magnetic fields due to currents in magnetostatics. We extend the range of applicability and the formal structure of the Biot-Savart law to electrostatics by deriving a Biot-Savart-like law suitable for calculating electric fields. We show that, under certain circumstances, the traditional Dirichlet problem can be mapped onto a much simpler Biot-Savart-like problem. We find an integral expression for the electric field due to an arbitrarily shaped, planar region kept at a fixed electric potential, in an otherwise grounded plane. As a by-product we present a very simple formula to compute the field produced in the plane defined by such a region. We illustrate the usefulness of our approach by calculating the electric field produced by planar regions of a few nontrivial shapes.