Force Generated by a Magnetic Field Applied on a Circular Conductive Turn Rotated in Two Cartesian Axes

This article presents a very detailed resolution of a non-trivial problem in Electromagnetic Theory. The problem basically consists of a circular conducting loop of radius R, which has a current I, and is located with its center at the origin of the Cartesian coordinate system. It is rotated with respect to the normal to its plane with angles of θ 0 and φ 0 in spherical coordinates, in addition, there is an applied External Magnetic Field. The forces generated by the magnetic field in all directions were calculated without approximations, where in the z direction the force is zero, as expected.