The problem of conjugation in calculations of electric field strength and potential of a ring-shaped multiply connected structure

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/S0735272707050093

Abstract

The paper proves the possibility for applying the problem of conjugation from the theory of functions of complex variables to determination of electric field intensity and potential in planar problems of electrostatics, particularly, in an open n-connected domain, in the case of a ring-shaped multiply connected boundary. The general expressions are deduced for the electric field strength and potential as applied to an arbitrary structure of a bordering ring-shaped line.

References

M. A. Lavrent’yev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable (Lan’, Sent-Petersburg, 2002) [in Russian].

N. I. Muskhelishvili, Singular Integral Equations: Boundary Problems of the Theory of Functions and Their Applications to Mathematical Physics (Nauka, Moscow, 1968) [in Russian].

F. D. Gakhov, The Boundary Problems (Nauka, Moscow, 1977) [in Russian].

N. P. Vekua, Systems of Singular Integral Equations and Some Boundary Problems (Nauka, Moscow, 1970) [in Russian].

L. I. Sedov, Planar Problems of Hydrodynamics and Aerodynamics (Nauka, Moscow, 1970) [in Russian].

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Published

2007-05-09

Issue

Vol. 50 No. 5 (2007)

Section

Research Articles