Calculation of magnetic force between two circular filaments arbitrary oriented in the space by using method of mutual inductance

A set of formulas for calculation of magnetic force between two circular filaments arbitrarily oriented in space were derived by using Mutual Inductance Method (MIM) (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 (Babic’s Method (BM)). The derived new formulas were validated via comparison with a series of reference examples.