Magnetic Force and Torque Calculation Between Circular Coils With Nonparallel Axes

A method for calculating the magnetic force and torque between circular coils with nonparallel axes and rectangular cross section is presented. In the method, the magnetic field values are expressed in terms of the complete elliptical integrals of the first and second kind. The magnetic force and torque results are obtained by adding all magnetic forces and torques of the filaments. The method can apply to all circumstances between the two circular coils in a vacuum permeability environment. In addition, another comparative method based on mutual inductance gradient is given. The accuracy of the method is discussed in this paper. Results obtained by the two approaches are in excellent agreement.