  Neutrinos with a magnetic moment $\mu$ change their helicity when interacting
with an electromagnetic field. Various aspects of this effect have been
described as spin precession, spin-flip scattering, and magnetic Cherenkov
radiation. These perspectives are unified in an expression for the
$\nu_L\to\nu_R$ transition rate which involves the correlators of the
electromagnetic field distribution. Our general formula corrects a previous
result and generalizes it to the case where the fields cannot be viewed as
classical and where the momentum transfers need not be small. We evaluate our
result explicitly for a relativistic QED plasma and determine the
depolarization rate to leading order in the fine structure constant. Assuming
that big-bang nucleosynthesis constraints do not allow a right-handed neutrino
in equilibrium we derive the limit $\mu<6.2\EE{-11}\mu_B$ on the neutrino
magnetic moment. Bounds on $\mu$ from a possible large scale magnetic fields
are found to be more stringent even for very weak fields
