There exist evidences that magnetic field in
the vicinity of astrophysical black holes plays an important role. In
particular it is required for explanation of such phenomenon as jet formation.
Study of such problems in all their complexity requires 3D numerical
simulations of the magnetohydrodynamics in a strong gravitational field. Quite
often when dealing with such a complicated problem it is instructive to
consider first its simplifications, which can be treated either analytically,
or by integrating ordinary differential equations. Motion of a charged particle
in a weakly magnetized black hole is an important example. We consider a
non-rotating black hole in the weak magnetic field which is homogeneous at infinity.
In the talk I discuss the following problems: How does such a magnetic field
affect charged particle motion in the equatorial plane? How does it change the
radius of the innermost stable circular orbits (ISCO) and period of rotation? I
shall demonstratethat the magnetic field increases the efficiency of the energy
extraction from the black hole and that magnetized black holes can be used as
"particle accelerators". Finally, I shall discuss
out-of-equatorial-plane motion and demonstrate that it is chaotic. Possible
applications of these results to astrophysics are briefly discussed.