  We discuss the role of general relativity frame dragging acting on magnetic
field lines near a rotating (Kerr) black hole. Near ergosphere the magnetic
structure becomes strongly influenced and magnetic null points can develop. We
consider aligned magnetic fields as well as fields inclined with respect to the
rotation axis, and the two cases are shown to behave in profoundly different
ways. Further, we construct surfaces of equal values of local electric and
magnetic intensities, which have not yet been discussed in the full generality
of a boosted rotating black hole.
