Description
Understanding and formally describing the motion of charged particles in magnetic fields is of great importance in several areas of the physical sciences. Despite this, little space is devoted to this issue in university textbooks. Moreover, the chosen approach is too idealized: it is restricted to non-viscous environments and focuses primarily on circular motion derived from the balance of magnetic and centripetal forces. In our contribution, we present a more comprehensive approach based on Newton’s equations of motion, providing deeper physical insights and paving the way for generalization to more realistic scenarios. We investigate the particle’s dynamics in viscous media, accounting for Stokes friction alongside the Lorentz force, and explicitly calculate trajectories, displacements, and angular momentum. Furthermore, we extend the consideration to Brownian motion using the classical Langevin equation with white thermal noise. Our findings reveal that the mean angular momentum (and consequently the magnetic moment) approaches a finite non-zero value in the long-time limit, leading to a discussion of how the results should be interpreted within the framework of classical statistical mechanics, in particular in relation to the assumptions underlying the Bohr–van Leeuwen theorem on the absence of classical magnetism. This approach serves as an effective pedagogical tool, bridging concepts from classical mechanics, statistical physics, and stochastic processes while encouraging student debate on the foundations of classical magnetism.