We extend the classical Avez-Seifert theorem to trajectories of charged test particles with fixed charge-to-mass ratio. In particular, given two events x_{ 0} and x_{ 1}, with x_{ 1} in the chronological future of x_{ 0}, we find an interval I=]-R,R[ such that for any q/m in I there is a timelike connecting solution of the Lorentz force equation. Moreover, under the assumption that there is no null geodesic connecting x_0 and x_1, we prove that to any value of |q/m| there correspond at least two connecting timelike solutions which coincide only if they are geodesics.
Categories: gr-qc