Sage Journals: Discover world-class research

Abstract

A general model for the calculation of current density in two parallel conductors is proposed. The solution of the model is based on the calculation of magnetic fluxes and on the application of Faraday's law of electromagnetic induction. Magnetic fluxes are determined via magnetic field integration. For this purpose, formulae are given in the Appendix Section for the calculation of the magnetic field produced by an infinitely long conductor the cross section of which is a sector of a ring. The proposed model is used to examine a pair of tubular conductors. The conductors are supplied from a source of sinusoidal voltage in steady state. It is assumed that the voltage frequency does not exceed 1 MHz, and the displacement current is neglected. Solutions to several problems are given. The effect of the resistivity of conductors, their distance and the source frequency on the current density and current in the conductors and on their series impedance is analysed. For the calculation of the inductance of distant tubular conductors very simple and exact formulae are derived, and the transient current in these conductors is described when the voltage source is connected and disconnected.

Keywords

Applied classical electromagnetism Faraday's law of induction transmission lines skin effect numerical methods

Get full access to this article

View all access options for this article.

References

Mayergoyz

I.D.

and Lawson

, Basic Electric Circuit Theory, Academic Press, New York, 1996, An Imprint of Elsevier.

IEC 60050-131:2002/A1:2008 International Electrotechnical Vocabulary - Part 131: Circuit theory.

Jackson

J.D.

, Classical Electrodynamics, 3rd edition, Wiley, New York, 1998.

IEC 60050-121:2000/A2:2010 International Electrotechnical Vocabulary - Part 121: Electromagnetism.

Reitz

J.R.

, Milford

F.J.

and Christy

R.W.

, Foundations of Electromagnetic Theory, Addison Wesley Longman, New York, 1993.

Stratton

J.A.

, Electromagnetic Theory, McGraw-Hill, New York and London, 1941.

Coufal

, Current density in a pair of solid coaxial conductors, Electromagnetics 27 (2007), 299-320.

Coufal

, On resistance and inductance of solid conductors, J. Eng. 2013 (2013), article No 526072; DOI: 10.1155/2013/526072.

Maxwell

J.C.

, A Treatise on Electricity and Magnetism, unabridged 3rd edition, vol. II Dover Publications, Inc., New York, 1954.

10.

Coufal

, On inductance and resistance of solitary long solid conductor, Acta Technica 57 (2012), 75-89.

11.

Coufal

, Current density in two solid parallel conductors and their impedance, Electr. Eng. 96 (2014), 287; DOI: 10.1007/s00202-014-0296-z.

12.

Ralston

and Rabinowitz

, A First Course in Numerical Analysis, Dover Publications, Mineola, New York, 2001.

13.

Lide

D.R.

, CRC Handbook of chemistry and physics, 88th edition, CRC Press, Boca Raton, 2007.

14.

Rektorys

and Vitásek

E (Editors), Survey of Applicable Mathematics, Kluwer, Dordrecht, 1994.

15.

Coufal

, Current density in a long solitary tubular conductor, J. Phys. A: Math. Theor. 41 (2008), article No 145401; DOI: 10.1088/1751-8113/41/14/145401.

16.

Mukoseev

Y.L.

, Distribution of alternating current in conductors (in Russian), Gosenergoizdat, Moscow, 1959.

17.

Compter

and Giaccone

, Analytical method for forces between current carrying infinite bars, COMPEL 35 (2016), 1281-1289.

18.

Dlabač

and Filipovič

, Integral equation approach for proximity effect in a two-wire line with round conductors, Technical Gazette 22 (2015), 1065-1068; DOI: 10.17559/TV-20140119140254.

19.

Coufal

, Current density in two parallel cylindrical conductors and their inductance, Electr. Eng. DOI: 10.1007/s00202-016-0378-1.

20.

Asner

, Berechnung und Anwendung von symmetrischen Multipolfeldern in zylindrischer Bohrung, erzeugt durch Sektorwicklungen konstanter Stromdichte, Bulletin SEV/VSE 64 (1973), 439-445.

21.

Gorenflo

and Welter

, Berechnung des ebenen Magnetfeldes parallerel Leiter endlicher Dicke mittels komplexer Analysis, Archiv für Elektrotechnik 51 (1967), 255-261.

22.

Coufal

, Forming the magnetic field by distribution of the current density in the coils for MHD generators, Acta Technica SAV 19 (1974), 299-316.

23.

Coufal

, Magnetic field and optimization of superconducting saddle-type coils of the magnet of MHD generator (in Czech), Studie SAV 22 (1986), ACADEMIA, Prague.

Faraday's law of electromagnetic induction in two parallel conductors

Abstract

Keywords

Get full access to this article

References