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PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2021-06-11
The Analytical Formula for Calculating the Self-Inductance for the Circular Coil of the Rectangular Cross-Section with a Non-Uniform Current Density
By
Slobodan Babic,

    Dr. Slobodan Babic

    Retired

    53 Berlioz, 101, H3E 1N2

    Canada

    Homepage

Matthew Smith,

    Dr. Matthew Smith

    Division of Engineering Programs at SUNY New Paltz

    USA

    Homepage

Nikiforos Fokas,

    Dr. Nikiforos Fokas

    Division of Engineering Programs at SUNY New Paltz

    USA

    Homepage

Yuriy Langer,

    Dr. Yuriy Langer

    Division of Engineering Programs at SUNY New Paltz

    USA

    Homepage

Jerry P. Selvaggi

    Dr. Jerry P. Selvaggi

    The Division of Engineering Programs at SUNY New Paltz

    USA

    Homepage

Progress In Electromagnetics Research M, Vol. 103, 15-26, 2021
doi:10.2528/PIERM21040905 | Google Scholar

Abstract
In this article we give an analytical formula for calculating the self-inductance for circular coils of rectangular cross-section which has a non-uniform current density. Recently, the formula for calculating this important electromagnetic quantity was published in the form of the single integral whose kernel function was asum of elementary functions. However, a new formula is obtained in the form of elementary functions, single integrals, and the complete elliptic integral of the first, second and third kind. Although its development looks tedious, we obtain a rather user-friendly expression for the calculation. From the general case, the self-inductance of the thin disk coil (pancake coil) with the nonuniform current is obtained in a remarkably simple form. The results of this work are compared with different known methods, and all results are in the excellent agreement. Our approach has not been found in the literature.
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Citation
Slobodan Babic, Matthew Smith, Nikiforos Fokas, Yuriy Langer, and Jerry P. Selvaggi, "The Analytical Formula for Calculating the Self-Inductance for the Circular Coil of the Rectangular Cross-Section with a Non-Uniform Current Density," Progress In Electromagnetics Research M, Vol. 103, 15-26, 2021.
doi:10.2528/PIERM21040905
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