Spatial potential of arbitrary uniformly charged polygons

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...

Full description

Saved in:
Bibliographic Details
Published in:European physical journal plus 2023-11, Vol.138 (11), p.1012, Article 1012
Main Authors: Sheng, Chen, Junyi, Lu, Xin, Chang, Yanyi, Wu, Baohua, Teng
Format: Article
Language:English
Subjects:
Apexes
Applied and Technical Physics
Atomic
Complex Systems
Condensed Matter Physics
Electric fields
Electric potential
Equivalence
Mathematical analysis
Mathematical and Computational Physics
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Polygons
Regular Article
Students
Superposition (mathematics)
Teaching
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-023-04644-4