Abstract
In this paper, the improved and the new analytical and semi-analytical expressions for calculating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air are given. The expressions are obtained either in the analytical form over the incomplete elliptic integrals of the first and the second kind 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 particular cases when the inclined circular loops are addressed. We mention that all formulas are obtained by the integral approach, except the stiffness, which is found by the derivative of the magnetic force. The novelty of this paper is the treatment of the inclined circular carting-current arc segments for which the calculations of the previously mentioned electromagnetic quantities are given.
Highlights
A field circular coil of arbitrary geometry may be made from finite circular current-carrying arc segments of the conductor for which the magnetic field can be calculated by the sum over the partial fields generated by each segment [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
All formulas are developed in the close form over the incomplete elliptic integrals of the first and the second kind and in the simple integral form whose kernel functions are given in the close form over the incomplete elliptic integrals of the first and the second kind
The magnetic vector potential and the magnetic field calculations are given in the analytical form expressed by the incomplete elliptic integrals of the first and second kind
Summary
A field circular coil of arbitrary geometry may be made from finite circular current-carrying arc segments of the conductor for which the magnetic field can be calculated by the sum over the partial fields generated by each segment [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Even though in the literature on can find many methods for calculating the magnetic vector potential and magnetic field of different current coils, we give the simplified formulas for calculating them, which will be the crucial auxiliary functions because they are given in the analytical form over the incomplete elliptic integrals of the first and second kind. In this paper we give a quite simple method for calculating the magnetic force and the mutual inductance between two inclined circular current-carrying arc segments in air, Physics 2021, 3 parallel axes.
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