  Dynamics of charged matter in the oblique black hole magnetosphere is
investigated. In particular, we adopt a model consisting of a rotating black
hole embedded in the external large-scale magnetic field that is inclined
arbitrarily with respect to the rotation axis. Breaking the axial symmetry
appears to have profound consequences regarding the dynamics of particles and
it also poses some methodological difficulties. In this contribution we discuss
the applicability of the method of effective potential for the non-axisymmetric
model and show that it may only be applied in the appropriate reference frame.
