  The aim of the present article is to evaluate the motion of charged test
particles in the vicinity of a near-extremal rotating black hole in the
presence of magnetic fields. Euler-Lagrange motion equations and effective
potential methods are used to characterize the motion out of the equatorial
plane. Such approach is of peculiar significance if it is considered, e.g.,
accretion processes onto rotating black holes. In general investigations
concerning accretion focus mostly on the simplest case of particles moving in
the equatorial plane. Here it will be considered that particles initially
moving around some particular orbit may be perturbed by a kick along the
$\theta$ direction, giving rise to other possible orbits. We confirm the
possibility that ultra high energy cosmic rays would be produced at the very
center of AGNs, for a specific range of magnetic field magnitudes, since it is
possible that ultra-high center-of-mass energies can be produced by particles
colliding near the horizon of fastly rotating black holes.
