In this article, formulas for calculation of magnetic 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 Babič’s expressions. The derived new formulas were validated via comparison with a series of reference examples. Also, we obtained additional expressions for 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.

本文利用 Kalantarov-Zeitlin 的方法推导了空间任意取向的两根圆丝之间的磁力和力矩的计算公式。公式通过积分表达式以解析形式呈现，其核函数用第一类和第二类椭圆积分表示，并提供了巴比奇表达式的替代公式。通过与一系列参考示例的比较来验证推导出的新公式。此外，我们通过对两个圆形灯丝之间的互感的格罗弗公式在适当坐标下的微分，获得了用于计算两个圆形灯丝之间的力和扭矩的附加表达式。