- We consider the dynamics of a charged active Brownian particle in three dimensions subjected to an external magnetic field. We show that, in the presence of a field gradient, a macroscopic flux emerges from a flux-free system and the density distribution becomes inhomogeneous. The flux is induced by the gradient of the magnetic field only and does not require additional symmetry breaking such as density or potential gradients. This stands in marked contrast to similar phenomena in condensed matter such as the classical Hall effect. We further demonstrate that passive tracer particles can be used to measure the essential effects caused by the Lorentz force on the active particle bath, and we discuss under which conditions this diffusive Hall-like effect might be observed experimentally.
