  In this paper, the orbits of a charged particle near the event horizon of a
magnetized black hole are investigated. For a static black hole of mass $M$
immersed in a homogeneous magnetic field $B$, the dimensionless parameter
$b=eBGM/ (mc^4)$ controls the radius of the circular orbits and determines the
position of the innermost stable circular orbit (ISCO), where $m$ and $e$ are
the mass and charge of the particle. For large values of the parameter $b$, the
ISCO radius can be very close to the gravitational radius. We demonstrate that
the properties of such orbits can be effectively and easily found by using a
properly constructed ``near-horizon approximation''. In particular, we show
that the effective potential (which determines the position of the orbit) can
be written in a form which is invariant under rescaling of the magnetic field,
and as a result is universal in this sense. We also demonstrate that in the
near-horizon approximation, the particle orbits are stationary worldlines in
Minkowski spacetime. We use this property to solve the equation describing slow
changes in the distance of the particle orbit from the horizon, which arise as
a result of the electromagnetic field radiated by the particle itself. This
allows us to evaluate the life-time of the particle before it reaches the ISCO
and ultimately falls into the black hole.
