By exploiting suitably a fundamental theorem by Hilbert, we show that the equation of motion of the electric charges is a consequence of Maxwell field equations.
Relativistic observer and Maxwell equations
Maxwell Equations in Complex Form of Majorana - Oppenheimer, Solutions with Cylindric Symmetry in Riemann S_{3} and Lobachevsky H_{3} Spaces
The Role of the Pauli-Lubanski Vector for the Dirac, Weyl, Proca, and Maxwell Equations
