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In this paper, we introduce a new algorithm for calculating the radial and axial magnetic forces between two non-coaxial circular loops with parallel axes. These formulas are derived from a modified version of Grover's formula for mutual inductance between the coils in question. Utilizing these formulas, we compute the radial and axial magnetic forces between two non-coaxial thick coils of rectangular cross-sections with parallel axes. In these calculations, we apply the filament method and conduct investigations to determine the optimal number of subdivisions for the coils in terms of computational time and accuracy. The method presented in this paper is also applicable to all conventional non-coaxial coils, such as disks, solenoids, and non-conventional coils like Bitter coils, all with parallel axes. This paper emphasizes the accuracy and computational efficiency of the calculations. Furthermore, the new method is validated according to several previously established methods. [ABSTRACT FROM AUTHOR]

In this paper we present a lucid, easy, and accurate approach for calculation of the mutual inductance between all inclined circular coils with either rectangular cross section or negligible section. We use Grover's formula for the mutual inductance between two filamentary circular coils with inclined axes that lie in the same plane. Their centers are either displaced along the axis of one coil or displaced along one axis of the first coil and then displaced sideways in addition. We apply the filament method for coil combinations comprising circular coils of rectangular cross section, thin wall solenoids, thin disk coils (pancakes), and filamentary circular coils. In this approach we clarify how Grover's formulas have to be used for different coil combinations in the filament treatment. Thus, two well-known methods (Grover's formulas and the filament method) can be easily used to calculate the mutual inductance between all inclined circular coils, even though the problem is purely three-dimensional. Index Terms--Circular coil of rectangular cross section, filament method, filamentary circular coil, mutual inductance, thin disk coil (pancakes), thin wall solenoid.

We present new and fast procedures for calculating magnetic forces between thin coaxial circular coaxial coils in air. The results are expressed in semianalytical form in terms of the complete elliptical integrals of the first and second kind, Heuman's Lambda function, and a term that must be solved numerically. These expressions are accurate and simple to use for several practical applications. We also describe a comparative method based on the filament technique. We discuss the computational cost and the accuracy of two methods and compare them with already published data. Results obtained by our two approaches are in excellent agreement with each other. They can be used in industrial electromagnetic applications such as electrodynamic levitation systems, linear induction launchers, linear actuators, and coil guns. Index Terms--Filamentary circular coil, magnetic force, thin disk coil, thin wall solenoid.

In this paper, we present analytic-numerical expressions for the calculation of the mutual inductance of two axisymetric circular coils with rectangular cross section in air. This original and new method may seem complicated but it is explicit, accurate, and fast, even though all expressions are obtained by the complete elliptic integrals of the first and second kind, Heuman's lambda function, and three terms that must be solved numerically. We confirm the validity of this approach by comparing it with other approaches (filament method and previously published data). We also compare the accuracy and the computational cost of this approach and that of the filament method. All results obtained by the various approaches are in excellent agreement. Index Terms--Filament method, Maxwell's coils, mutual inductance, Neumann's formula.

This paper presents an efficient method for computing the mutual inductance between two thin coaxial disk coils in air. The derived principal semi-analytical expressions involve complete elliptic integrals of the first and second kind, Heuman's Lambda function and three terms that have to be computed numerically. The presented method is compared to the filament method where both conductors are approximated by Maxwell's filamentary coils. The mutual inductance values (for a chosen case) computed by both methods are in good agreement. However, the method presented in this work exceeds by far the filament method in its precision and computational efficiency. In another example, the computed mutual inductance is validated by measurement. Index Terms--Mutual inductance, thin disk coils, Biot-Savart law, Maxwelrs coils.

In this paper, new expressions are presented for three-dimensional magnetic-field calculation for a massive disk currying radial currents. These expressions have been obtained in analytical form as functions of incomplete elliptical integrals (of the first, second, and third kind) and an integral to be solved numerically. This approach enables one to easily calculate the magnetic field everywhere in space at reduced computational cost. In addition, it can be employed to calculate the magnetic field in conductor disk configurations involving complicated geometry as well as to evaluate their self and mutual inductance. Index Terms--Biot-Savart law, magnetic field, radial current-carrying disks.

In this article we give an analytical formula for calculating the self-inductance for circular coils of rectangular cross-section which has a nonuniform current density. Recently, the formula for calculating this important electromagnetic quantity was published in the form of the single integral whose kernel function was a sum 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. [ABSTRACT FROM AUTHOR]

This paper deals with two efficient approaches for determining the mutual inductance between thin circular coils and disk coils in air. The first approach gives new expressions for calculating the mutual inductance of treated configurations. These results are expressed over the complete elliptical integrals of the first and second kind, Heuman's Lambda function, and one term that must be solved numerically. Another approach is based on the filament method where conductors are approximated by the set of Maxwell's coils. The obtained expressions are expressed over the complete elliptical integrals of the first and second kind and permit also fast calculation of the mutual inductance for mentioned systems. These new expressions are accurate and simple for useful applications. All results obtained by the two approaches are in excellent agreement. Index Terms--Biot-Savart law, circular coils, disk coils, Maxwell's coils, mutual inductance.

A new closed-form expression based on double integral computation is introduced for 3D magnetostatic fields of current-carrying solid conductors whose vector density satisfies the condition that its curl is zero. Such a reduced expression is derived for a torroidal conductor with radial current flow, solved analytically, and used for 3D field computation. For illustration, by applying the same reduction principle, the 3D magnetic fields are computed for cylindrical and rectangular conductors with longitudinal flowing current.

This paper presents a mathematical model for calculating 3D linear magnetostatic fields with open boundaries. By using this improved method (based on the integral equations and magnetic surface charge), several field computation problems inside magnetic materials are being avoided. A comprehensive procedure is established for magnetic field computation within the free space and iron, as well as on their boundary--at a reduced computational cost. The proposed method was compared to the analytical solution for a test case. Index Terms--Biot-Savart law, fictitious magnetic charge, integral method, magnetostatic field calculation.