  Circular motion of particles, dust grains and fluids in the vicinity of
compact objects has been investigated as a model for accretion of gaseous and
dusty environment. Here we further discuss, within the framework of general
relativity, figures of equilibrium of matter under the influence of combined
gravitational and large-scale magnetic fields, assuming that the accreted
material acquires a small electric charge due to interplay of plasma processes
and photoionization. In particular, we employ an exact solution describing the
massive magnetic dipole and we identify the regions of stable motion. We also
investigate situations when the particle dynamics exhibits the onset of chaos.
In order to characterize the measure of chaoticness we employ techniques of
Poincar\'e surfaces of section and of recurrence plots.
