Helical buckling of a whirling conducting rod in a uniform magnetic field

► We study the post-buckling behaviour of a whirling conducting rod in a uniform magnetic field. ► We present new boundary conditions subject to which the rod buckles into a helix. ► We propose a mechanical device for generating helical solutions in the laboratory. ► We obtain a surprisingly simple exact formula for the critical buckling load. ► We find various secondary (oscillatory) instabilities described by Hopf bifurcations.