Inverse problem of relativistic mechanics for a test charge in an external static field

We consider the motion of an electrically charged test particle in static spacetime when it is necessary to reconstruct the electromagnetic field tensor. The problem is solved for the two special cases when the electromagnetic field reduces to an electrostatic field or a magnetostatic one. It is shown that the electrostatic field can be determined within a single arbitrary function, and the magnetostatic field within two such functions.Translated from Izvestiya Vysskikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 67–70, February, 1982.