A didactic development to determinate the solution of the motion equations for a charged particle under influence of electric and magnetic static and homogeneous fields is proposed. Our proposed uses the advantages and proprieties of the Laplace's transformation, to map a system of N non-homogeneous differential equations of second order in a system composed by N linear equations. From the solution more general for dynamics of the system, we study some particular cases to recover, of a simple way, the results present in the literature. In order to give a motivation to our study, we use the Ehrenfest's theorem and we discuss as the classical results can be interpreted in its quantum version.
Keywords:
Charge moving; electric and magnetic fields; trajectory; quantum analogue
