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

Abstract

In this article, formulas for the 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 an analytical form through integral expressions, whose kernel function is expressed in terms of the elliptic integrals of the first and second kinds, and provide an alternative formulation to Babic's expressions. The derived new formulas were validated via comparison with a series of reference examples. Also, we obtained additional expressions for the calculation of force and torque between two circular filaments by means of differentiation of Grover's formula for the mutual inductance between two circular filaments with respect to appropriate coordinates. These additional expressions allow to verifying comprehensively and independently derived new formulas.