Lorentz force-induced stresses in long current-carrying conductors

Technique for calculation of Lorentz force-induced stresses in long straight conductors with the uniform current density in the presence of an external magnetic field is proposed. Reduction of the plane elastic problem for the conductor of a narrow rectangular cross section embedded in an arbitrary external field to the known homogeneous problems is considered. As an example stress analysis of an elliptical conductor with the stress-free lateral surface under the interaction of the current with its self field is performed and particular solutions of the problem of the interaction with the external field produced by the current flowing in an analogous conductor are given.