  We investigate the time dependent orbital diamagnetic moment of a charged
particle in a magnetic field in a viscous medium via the Quantum Langevin
Equation. We study how the interplay between the cyclotron frequency and the
viscous damping rate governs the dynamics of the orbital magnetic moment in the
high temperature classical domain and the low temperature quantum domain for an
Ohmic bath. These predictions can be tested via state of the art cold atom
experiments with hybrid traps for ions and neutral atoms. We also study the
effect of a confining potential on the dynamics of the magnetic moment. We
obtain the expected Bohr Van Leeuwen limit in the high temperature, asymptotic
time ($ \gamma t\longrightarrow \infty$, where $ \gamma $ is the viscous
damping coefficient) limit.
