  Understanding the mechanisms of particle acceleration from the vicinity of
black holes poses a challenge. Electromagnetic effects are thought to be a
prime suspect, but details still need an explanation. To this end, we study a
three-dimensional structure of oblique magnetic fields near a rotating black
hole in vacuum. It has been proposed that such a set-up can lead to efficient
acceleration when plasma is injected near a magnetic null point. We focus our
attention especially on the magnetic field in the immediate neighborhood of the
magnetic null point, which was previously shown to occur in the equatorial
plane. By employing the Line-Integral-Convolution (LIC) method, we visualize
the magnetic field lines and explore the electric lines rising out of the
equatorial plane. We show the magnetic field structure near the boundary of
ergosphere, depending on the spin of the black hole. Electric field develops a
non-vanishing component passing through the magnetic null point and ensuring
efficient acceleration of charged particles from this particular location near
horizon. We also examine the effect of translatory boost on the field lines.
Similarly to the frame-dragging by rotation, the linear motion carries field
lines along with the black hole. Position of the magnetic null point recedes
from the black hole horizon as the spin parameter increases. For the extreme
value of a=1 the null point can occur outside the ergosphere.
