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Electric and magnetic fields of two infinitely long parallel cylindrical conductors carrying a DC current*

Published online by Cambridge University Press:  08 November 2013

Kristof Engelen ,
Pieter Jacqmaer  and
Johan Driesen
Kristof Engelen
Affiliation:
University of Leuven, Department of Electrical Engineering, Kasteelpark Arenberg 10, 3001 Heverlee, Belgium
Pieter Jacqmaer*
Affiliation:
University of Leuven, Department of Electrical Engineering, Kasteelpark Arenberg 10, 3001 Heverlee, Belgium
Johan Driesen
Affiliation:
University of Leuven, Department of Electrical Engineering, Kasteelpark Arenberg 10, 3001 Heverlee, Belgium
*
ae-mail: pieter.jacqmaer@skynet.be
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Abstract

This paper calculates the electric and magnetic fields and the Poynting vector around two infinitely long parallel cylindrical conductors, carrying a DC current. Also the charges on the surface of the wire are calculated, and their distribution is visualized. The wire is assumed to be perfectly electrically conducting. Furthermore, the Hall effect is ignored. In the literature [S.J. Orfanidis, Electromagnetic waves and antennas, 2008], the problem of determining the electric field is usually tackled using an equivalent model consisting of two line charge densities, producing the same electric field. In this work, the Laplace equation is rigorously solved. The authors found no work explaining the solution of the Laplace equation with boundary conditions for this problem and hence thought it was useful to dedicate a paper to this topic. The method of separation of variables is employed and a bipolar coordinate system is used. After solving the appropriate Sturm-Liouville problems, the scalar potential is obtained. Taking the gradient yields the electric field.

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 64 , Issue 2 , November 2013 , 24515
Copyright
© EDP Sciences, 2013

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Footnotes

*

Contribution to the Topical Issue “Numelec 2012”, Edited by Adel Razek.

References

Orfanidis, S.J., Electromagnetic waves, antennas, 2008, chap. 10, Available online: www.ece.rutgers.edu/orfanidi/ewaGoogle Scholar
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Weinberger, H.F., A First Course in Partial Differential Equations (Xerox College Publishing, Lexington, MA, 1965)Google Scholar
Stratton, J.A., Electromagnetic Theory (McGraw-Hill, New York and London, 1941), pp. 55–56Google Scholar
Assis, A.K.T., Hernandes, J.A., The Electric Force of a Current: Weber and the Surface Charges of Resistive Conductors Carrying Steady Currents (Apeiron, Montreal, 2007)Google Scholar