LAUSR

In this work we present the original Langevin's method to study the Brownian motion of a charged particle across a constant magnetic field. Langevin's strategy allows transforming the Langevin equation into a deterministic one associated with Mean Square Displacement (MSD), whose solution is explicitly study in this work. We calculate the MSD for the $z$-axis, along which the magnetic field is allowed to point, in this direction, the solution is exactly the same proposed by Langevin. While, in the $x$-$y$ plane orthogonal to the magnetic field, the solution for the MSD is obtained with the validity of the Bohr-van Leuuwen theorem in thermal equilibrium.