Vol. 103

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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, Matthew Smith, Nikiforos Fokas, Yuriy Langer, and Jerry P. Selvaggi
Progress In Electromagnetics Research M, Vol. 103, 15-26, 2021
doi:10.2528/PIERM21040905

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.

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
http://jpier.org/PIERM/pier.php?paper=21040905

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