Brownian motion of a charged particle in a magnetic field

In this work we show that Taylor's description of Brownian motion in a magnetic field is equivalent to the situation in which the constant magnetic field is allowed to point along any direction. This can be achieved by means of a rotation of the Langevin equation given in the space of coordinates r, to another space of coordinates r', where the description of the problem is quite similar to that studied by Taylor. We use the over-damping approximation to show why, at equilibrium, the oscillatory behavior inherent in the system is not reflected in the diffusion process across the magnetic field, a fact not studied by Taylor. We also use the large-time approximation to study the effects of colored noise (small correlation time) on the diffusion processes across and along the magnetic field.