  We consider random primordial magnetic fields and discuss their dissipation,
coherence length $L_0$, scaling behaviour and constraints implied by the
primoridal nucleosynthesis. Such magnetic fields could excite the
right-helicity states of Dirac neutrinos, with adverse consequences for
nucleosynthesis. We present solutions to the spin kinetic equation of a Dirac
neutrino traversing a random magnetic field in the cases of large and small
$L_0$, taking also into account elastic collisions. Depending on the scaling
behaviour and on the magnetic coherence length, the lower limit on the neutrino
magnetic moment thus obtained could be as severe as $10^{-20}\mu_B$.
