https://doi.org/10.1140/epjp/s13360-023-04644-4
Regular Article
Spatial potential of arbitrary uniformly charged polygons
1
School of Physics, University of Electronic Science and Technology of China, 611731, Chengdu, People’s Republic of China
2
Yingcai Experimental School, University of Electronic Science and Technology of China, 611731, Chengdu, People’s Republic of China
Received:
29
August
2023
Accepted:
31
October
2023
Published online:
13
November
2023
In this paper, a unified analytical method for calculating the potential of any uniformly charged polygon is proposed. The principle of dividing an arbitrary N-sided polygon into N triangles is firstly determined by using the superposition theorem. Then the plane electric potential of the uniformly charged N-sided polygon is equivalent to the electric potentials at the vertices of N triangles, and further the space electric potential of the uniformly charged N-sided polygon is equivalent to the electric potentials on the perpendicular lines at the vertices of N triangles. As an application of this method, the analytical expressions for the center and vertex potentials of a uniformly charged regular N-sided polygon are obtained, and the equipotential lines of the plane and space potentials of an arbitrary N-sided polygon are plotted. The results show that the equipotential lines can always reflect the shape characteristics of charged bodies.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
