Properties of the multipole fields formed by round electrodes

The aim of the work is to study the properties of multipole electric fields formed by round rods. We consider the problem of finding the convergence radius of the series obtained by expansion of the potential into spatial harmonics, as well as the calculation of the complex potential for the case of the optimal configuration of cylindrical electrodes. A method is given for finding the real potential, which allows to obtain expansion of potential into power series with high precision.

Automated summary

The aim of this work is to study the properties of multipole electric fields generated by cylindrical electrodes. The study considers the convergence radius of the series expansion of electric potential into spatial harmonics and calculates the complex potential for the optimal configuration of the cylindrical electrodes. Additionally, a method is presented for accurately obtaining the expansion of potential into power series.