Applying Conformal Mapping to Determine the Electric Field of a Non-Concentric Cylindrical Capacitor and Its Capacitance

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.