Magnetic fields have become an essential ingredient of black hole astrophysics. The study of simplified models of magnetized black holes can shed light on some of the complicated phenomena observed near astrophysical black holes. In this thesis we studied the three-dimensional motion of charged particles in the background of Schwarzschild and Kerr black holes immersed in a weak uniform axisymmetric magnetic field. We studied in particular the escape of charged particles after they are kicked out of circular orbits.;It was not possible to give analytical conditions for charged particles escape. The magnetic field renders their equations of motion non-integrable in general. Numerical study of the problem revealed that the dynamics of charged particles near magnetized black holes is generally chaotic. With the help of the basin of attraction approach, we could give empirical formulae for guaranteed escape. We found that the final fate of a charge particle is nearly determined by its proximity to the black holes. No general relationship between the chaoticness in the dynamics and black hole rotation could be found.;We started with neutral particles and gave analytical conditions for their escape. Unlike with the Schwarzschild black hole, the escape conditions were non-trivial when the black hole is rotating where escape depends essentially on the particle initial position.
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