  We study the motion of a charge on a conformally flat Riemannian torus in the
presence of magnetic field. We prove that for any non-zero magnetic field there
always exist orbits of this motion which have conjugate points. We conjecture
that the restriction of conformal flatness of the metric is not essential for
this result. This would provide a ``twisted'' version of the recent
generalisation of Hopf's rigidity result obtained by Burago and Ivanov.
