  We study the electromagnetic vertex function of a neutrino that propagates in
an electron background in the presence of a static magnetic field. The
structure of the vertex function under the stated conditions is determined and
it is written down in terms of a minimal and complete set of tensors. The
one-loop expressions for all the form factors is given, up to terms that are
linear in the magnetic field, and the approximate integral formulas that hold
in the long wavelength limit are obtained. We discuss the physical
interpretation of some of the form factors and their relation with the concept
of the neutrino induced charge. The neutrino acquires a longitudinal and a
transverse charge, due to the fact that the form factors depend on the
transverse and longitudinal components of the photon momentum independently. We
compute those form factors explicitly in various limiting cases and find that
the longitudinal and transverse charge are the same for the case of a
non-relativistic electron gas, but not otherwise.
