Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 23 September 2021 / Approved: 24 September 2021 / Online: 24 September 2021 (12:56:12 CEST)

How to cite: Babic, S. Vector Potential, Magnetic Field, Mutual Inductance, Magnetic Force, Torque and Stiffness Calculation between Current-Carrying Arc Segments with Inclined Axes in Air. Preprints 2021, 2021090435 (doi: 10.20944/preprints202109.0435.v1). Babic, S. Vector Potential, Magnetic Field, Mutual Inductance, Magnetic Force, Torque and Stiffness Calculation between Current-Carrying Arc Segments with Inclined Axes in Air. Preprints 2021, 2021090435 (doi: 10.20944/preprints202109.0435.v1).

## Abstract

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 stiffness between two inclined current-carrying arc segments in air. The expressions are ob-tained either in the analytical form over the incomplete elliptic integrals of the first and the sec-ond time or by the single numerical integration of some elliptical integrals of the first and the second kind. The validity of the presented formulas is proved from the special cases when the inclined circular loops are treated. We mention that all formulas are obtain by the integral ap-proach except the stiffness which is found by the derivative of the magnetic force.

## Keywords

Magnetic vector potential; magnetic field; mutual inductance; magnetic force; torque; stiffness

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