Faraday's law of electromagnetic induction in two parallel conductors

Article type: Research Article

Authors: Coufal, Oldřich

Affiliations: Brno University of Technology, Technická 3082/12, Brno 61600, Czech Republic. E-mail: [email protected]

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

DOI: 10.3233/JAE-160123

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 54, no. 2, pp. 263-280, 2017