Potential magnetic fields around flux ropes

A method of calculation of potential magnetic fields around cylindrical and toroidal flux ropes is presented. The flux rope has an arbitrary orientation with respect to ambient field. The problem is solved analytically. Expressions for the magnetic field components, diamagnetic force, and its moment are found. Results obtained can be used for estimations of magnetic forces in systems where magnetic flux ropes and potential fields coexist, e.g., in the solar corona.