Applying Conformal Mapping to Determine the Electric Field of a Non-Concentric Cylindrical Capacitor and Its Capacitance
- 1 University College, The Pennsylvania State University, York, USA
Abstract
A cylindrical capacitor’s electric field of non-concentric double circular shells is determined and graphed by applying conformal mapping. It is demonstrated, using the Computer Algebra System (CAS) Mathematica , primarily numerically, how the lack of symmetry in the configuration is addressed and handled. Numerically, various essential properties of the applied conformal transformation are investigated. This article examines the relationship between the associated capacitance and the separation distance between the centers of the shells. It reveals its unexpected, peculiar behavior at a certain separation distance between the shells. Numerous quantities of interest are graphed visually in the mentioned electric field between the shells, enhancing the understanding of the issues at hand. The article embodies Mathematica codes, enabling their reproduction and enriching and deepening the field of interest.
- Jackson, J.D. (1999) Classical Electrodynamics. 3rd Edition, Wiley.
- Mathematica R V14.1. http://Wolfram.com
- Sokolnikoff, I.S. and Redheffer, R.M. (1966) Mathematics of Physics and Modern Engineering. 2nd Edition, McGraw-Hill.
- Kober, H. (1960) Dictionary of Conformal Mappings. Dover Publications.
- Schinzinger, R. and Laura, P.A.A. (2003) Conformal Mapping: Methods and Applications. Dover Publications.
- Asmar, M.H. and Grafakos, L. (2018) Complex Analysis with Applications. Springer.
- Wolfram, S. (2003) The Mathematica Book. 5th Edition, Cambridge University Publications.
- Sarafian, H. (2019) Mathematica Graphics Examples. 2nd Edition, Scientific Search Publishing.
- Sarafian, H. (2023) Haiduke Sarafian’s Collective Articles 2020-2023. Scientific Research Search Publishing.