# Magnetic Stiffness Calculation for the Corresponding Force between Two Current-Carrying Circular Filaments Arbitrarily Oriented in the Space

@article{Poletkin2022MagneticSC, title={Magnetic Stiffness Calculation for the Corresponding Force between Two Current-Carrying Circular Filaments Arbitrarily Oriented in the Space}, author={Kirill V. Poletkin and Slobodan Babic}, journal={SSRN Electronic Journal}, year={2022} }

In this article, sets of analytical formulas for calculation of nine components of magnetic stiffness of corresponding force arising between two current-carrying circular filaments arbitrarily oriented in the space are derived by using Babic’s method and the method of mutual inductance (Kalantarov-Zeitlin’s method). Formulas are presented through integral expressions, whose kernel function is expressed in terms of the elliptic integrals of the first and second kinds. Also, we obtained an…

## One Citation

### Calculation of Mutual Inductance between Circular and Arbitrarily Shaped Filaments via Segmentation Method

- Physics
- 2022

—In this article, two analytical formulas for the calcu- lation of mutual inductance between a circular ﬁlament and line segment arbitrarily positioning in the space are derived by using Mutual…

## References

SHOWING 1-10 OF 44 REFERENCES

### Calculation of force and torque between two arbitrarily oriented circular filaments using Kalantarov-Zeitlin's method

- Engineering
- 2021

In this article, formulas for calculation of force and torque between two circular filaments arbitrarily oriented in space were derived by using Kalantarov-Zeitlin’s method. Formulas are presented in…

### Magnetic Force Between Inclined Circular Filaments Placed in Any Desired Position

- PhysicsIEEE Transactions on Magnetics
- 2012

This paper presents new general formulas for calculating the magnetic force between inclined circular filaments placed in any desired position. We use two approaches to calculate the magnetic force,…

### Efficient calculation of the mutual inductance of arbitrarily oriented circular filaments via a generalisation of the Kalantarov-Zeitlin method

- PhysicsJournal of Magnetism and Magnetic Materials
- 2019

### Vector Potential, Magnetic Field, Mutual Inductance, Magnetic Force, Torque and Stiffness Calculation between Current-Carrying Arc Segments with Inclined Axes in Air

- PhysicsPhysics
- 2021

In this paper we give the improved and new analytical and semi-analytical expression for calcu-lating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and…

### Mutual Inductance Calculation Between Circular Filaments Arbitrarily Positioned in Space: Alternative to Grover's Formula

- MathematicsIEEE Transactions on Magnetics
- 2010

In this paper, we present the full derivation of a new formula for calculating the mutual inductance between inclined circular filaments arbitrarily positioned with respect to each other. Although…

### Magnetic Force Calculation Between Circular Coils of Rectangular Cross Section with Parallel Axes for Superconducting Magnet

- Physics
- 2012

The electromagnetic force between two misaligned coils (coils with parallel axes) with uniform current density distribution and rectangular cross section based on the derived semi-analytical…

### MUTUAL INDUCTANCE AND FORCE EXERTED BETWEEN THICK COILS

- Physics
- 2010

We present exact three-dimensional semi-analytical ex- pressions of the force exerted between two coaxial thick coils with rect- angular cross-sections. Then, we present a semi-analytical formulation…

### Magnetic Force Calculation Between Thin Coaxial Circular Coils in Air

- PhysicsIEEE Transactions on Magnetics
- 2008

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…

### A New Methodology for Magnetic Force Calculations Between Planar Spiral Coils

- Physics
- 2009

Due to the special structure of current carrying planar spiral coils, precise calculation of the forces between them is complicated and time-consuming. To overcome these problems, in this paper a new…

### MAGNETIC FORCE BETWEEN INCLINED CIRCULAR LOOPS (LORENTZ APPROACH)

- Physics, Engineering
- 2012

This paper presents a new general formula for calculating the magnetic force between inclined circular loops placed in any desired position. This formula has been derived from the Lorentz force…