  We present a computation of the charge and the magnetic moment of the
neutrino in the recently developed electro-weak Background Field Method and in
the linear $R_{\xi}^L$ gauge. First, we deduce a formal Ward-Takahashi identity
which implies the immediate cancellation of the neutrino electric charge. This
Ward-Takahashi identity is as simple as that for QED. The computation of the
(proper and improper) one loop vertex diagrams contributing to the neutrino
electric charge is also presented in an arbitrary gauge, checking in this way
the Ward-Takahashi identity previously obtained. Finally, the calculation of
the magnetic moment of the neutrino, in the minimal extension of the Standard
Model with massive Dirac neutrinos, is presented, showing its gauge parameter
and gauge structure independence explicitly.
