  In this paper we have presented the mechanism of the barrier crossing
dynamics of a Brownian particle which is coupled to a thermal bath in the
presence of both time independent and fluctuating magnetic fields. Here the
following three aspects are important in addition to the role of the thermal
bath on the barrier crossing dynamics. Magnetic field induced coupling may
introduce a resonance like effect. Another role of the field is that
enhancement of its strength reduces the frequency factor of the barrier
crossing rate constant. Finally, the fluctuating magnetic field introduces an
induced electric field which activates the Brownian particle to cross the
energy barrier. As a result of interplay among these aspects versatile
non-monotonic behavior may appear in the variation of the rate constant as a
function of the strength of the time independent magnetic field.
