Magnetic stiffness calculation for the corresponding force between two currentcarrying circular filaments arbitrarily oriented in the space
Abstract
In this article, sets of analytical formulas for calculation of nine components of magnetic stiffness of corresponding force arising between two currentcarrying circular filaments arbitrarily oriented in the space are derived by using Babic's method and the method of mutual inductance (KalantarovZeitlin'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 additional set of expressions for calculation of components of magnetic stiffness by means of differentiation of Grover's formula of the mutual inductance between two circular filaments with respect to appropriate coordinates. The derived sets of formulas were mutually validated and results of calculation of components of magnetic stiffness agree well to each other.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.04650
 Bibcode:
 2022arXiv220104650P
 Keywords:

 Physics  Applied Physics
 EPrint:
 40 pages, 12 figures. arXiv admin note: text overlap with arXiv:2106.09496