  We consider a certain extension of the Einstein's elevator thought experiment
by assuming that the elevator is charged and falls into an electromagnetic
field. We argue, on grounds of the Equivalence Principle, that an
observer-dependent metric should exist, for which the geodesics coincide with
the trajectories of the charged body in the electromagnetic field. We give a
solution to this problem by finding such a metric and hence we are able to
recover the Lorentz-force law. Recovery of the leading terms of the radiation
reaction force is also possible with this approach.
