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Addendum published on 18 January 2021, see Physics 2021, 3(1), 1-5.
Article

Self-Inductance of the Circular Coils of the Rectangular Cross-Section with the Radial and Azimuthal Current Densities

1
Independent Researcher, 53 Berlioz, 101, Montréal, QC H3E 1N2, Canada
2
École Polytechnique, C.P. 6079 Centre-Ville, Montréal, QC H3C 3A7, Canada
*
Author to whom correspondence should be addressed.
Physics 2020, 2(3), 352-367; https://doi.org/10.3390/physics2030019
Received: 15 June 2020 / Revised: 3 July 2020 / Accepted: 6 July 2020 / Published: 13 July 2020
(This article belongs to the Section Applied Physics)
In this paper, we give new formulas for calculating the self-inductance for circular coils of the rectangular cross-sections with the radial and the azimuthal current densities. These formulas are given by the single integration of the elementary functions which are integrable on the interval of the integration. From these new expressions, we can obtain the special cases for the self-inductance of the thin-disk pancake and the thin-wall solenoids that confirm the validity of this approach. For the asymptotic cases, the new formula for the self-inductance of the thin-wall solenoid is obtained for the first time in the literature. In this paper, we do not use special functions such as the elliptical integrals of the first, second and third kind, nor Struve and Bessel functions because that is very tedious work. The results of this work are compared with already different known methods and all results are in excellent agreement. We consider this approach novel because of its simplicity in the self-inductance calculation of the previously-mentioned configurations. View Full-Text
Keywords: self-inductance; radial current; azimuthal current; thick coils; disk coils; solenoids self-inductance; radial current; azimuthal current; thick coils; disk coils; solenoids
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MDPI and ACS Style

Babic, S.; Akyel, C. Self-Inductance of the Circular Coils of the Rectangular Cross-Section with the Radial and Azimuthal Current Densities. Physics 2020, 2, 352-367. https://doi.org/10.3390/physics2030019

AMA Style

Babic S, Akyel C. Self-Inductance of the Circular Coils of the Rectangular Cross-Section with the Radial and Azimuthal Current Densities. Physics. 2020; 2(3):352-367. https://doi.org/10.3390/physics2030019

Chicago/Turabian Style

Babic, Slobodan; Akyel, Cevdet. 2020. "Self-Inductance of the Circular Coils of the Rectangular Cross-Section with the Radial and Azimuthal Current Densities" Physics 2, no. 3: 352-367. https://doi.org/10.3390/physics2030019

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