Calculation of the Electrostatic Field of a Circular Cylinder with a Slot by the Wiener–Hopf Method

Seitkerim B. Bimurzaev, Seil S. Sautbekov, Zerde Sautbekova

Mathematics, 2023

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DOI 10.3390/math11132933
Data confidence 70 medium
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Abstract

The article considers an internal boundary value problem of the distribution of an electrostatic field in a lens formed by two identical semi-infinite circular cylinders coaxially located inside an infinite external cylinder. The problem is reduced to solving a system of singular Wiener-Hopf integral equations, which is further solved by the Wiener-Hopf method using factorized Bessel functions. Solutions to the problem for each region inside the infinite outer cylinder are presented as exponentially converging series in terms of eigenfunctions and eigenvalues.