Calculation of mutual inductance and magnetic force between two inclined circular coils of rectangular cross-section positioned in any desired position

This paper introduces new formulas for calculating the mutual inductance and components of the magnetic force between two inclined circular coils with rectangular cross-sections positioned in any orientation in free space. We apply the filament method and conduct investigations to determine the optimal number of subdivisions for the coils in terms of computational time and accuracy. The method presented is also applicable to conventional non-coaxial coils, such as disks, solenoids, and non-conventional coils like Bitter coils, positioned in any desired orientation in free space. This paper emphasizes the accuracy and computational efficiency of the calculations, addressing the scarcity of existing methods in the literature on this topic. Furthermore, the new method is validated against established methods found in the literature, which are scarce.