Representation of electric field strength and potential in the region with circular n-connection boundary as a sum of space harmonics

Authors

  • Yu. F. Zin'kovskii National Technical University of Ukraine "Kyiv Polytechnic Institute", Ukraine
  • Yu. K. Sidoruk National Technical University of Ukraine "Kyiv Polytechnic Institute", Ukraine
  • A. V. Goloshchapov National Technical University of Ukraine "Kyiv Polytechnic Institute", Ukraine

DOI:

https://doi.org/10.3103/S0735272709070024

Abstract

The possibility and reasonability of representing the electric field strength and potential on an open complex plane with n-connected circular boundary and equal lengths of bounding arcs as a sum of space harmonics is shown. Analysis on presence or absence of space harmonics is conducted and their amplitudes are calculated.

References

  1. Yu. F. Zin’kovskii, Yu. K. Sidoruk, and А. V. Goloshchapov, “The problem of conjugation in calculations of electric field strength and potential of a ring-shaped multiply connected structure,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 50(5), 76 (2007) [Radioelectron. Commun. Syst. 50(5), 284 (2007)].
  2. Yu. F. Zin’kovskii, Yu. K. Sidoruk, and A. V. Goloshchapov, “Electric field density in the region with circular multiply connected border and equal lengths of bounding arcs,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 52(2), 14 (2009) [Radioelectron. Commun. Syst. 52(2), 63 (2009)].
  3. L. D. Goldstein and N. V. Zernov, Electromagnetic Fields and Waves (Moscow, Sov. Radio, 1971) [in Russian].
  4. I. S. Gradshtein and I. М. Ryzhik, Tables of Integrals, Sums, Series and Products (Moscow, Nauka, 1971) [in Russian].
  5. Е. Yanke, F. Emde, and F. Lesh, Special Functions (Formulas, Graphs, Tables) (Moscow, Nauka, 1968) [in Russian].
  6. М. А. Lavrent’ev and B. V. Shabat, Methods of Complex Variable Functions Theory (St. Petersburg, Lan’, 2002) [in Russian].
  7. N. I. Muskhelishvili, Singular Integral Equations: Boundary Problems of the Functions Theory and Some Their Application to Mathematical Physics (Moscow, Nauka, 1968) [in Russian].
  8. F. D. Gakhov, Boundary Problems (Moscow, Nauka, 1977) [in Russian].

Downloads

Published

2009-07-02

Issue

Vol. 52 No. 7 (2009)

Section

Research Articles