  Electron polarization induced by magnetic fields can modify the potentials
relevant for describing neutrino conversions in media with magnetic fields. The
magnitudes of polarization potentials are determined for different conditions.
We show that variations of the electron polarization along the neutrino
trajectory can induce resonant conversions in the active-sterile neutrino
system, but cannot lead to level crossing in the active-active neutrino system.
For neutrino flavour conversions the polarisation leads only to a shift of the
standard MSW resonance. For polarizations $\lambda \lsim 0.04$ the direct
modifications of the potential (density) due to the magnetic field pressure are
smaller than the modifications due to the polarization effect. We estimate that
indeed the typical magnitude of the polarization in the sun or in a supernova
are not expected to exceed $10^{-2}$. However even such a small polarization
may lead to interesting consequences for supernova physics and for properties
of neutrino signals from collapsing stars.
