Induced Charge of Neutrinos in a Medium

Neutrinos can polarize a medium due to their weak interaction. This can manifest itself as an effective induced charge of the neutrino. We show how it is related to the Debye screening length in a plasma, first using the results of the 1-loop calculation of the neutrino electromagnetic vertex and then in general to all orders in $e$ and to leading order in the Fermi coupling. We also discuss how the results are modified if the neutrinos have mass -- either Dirac or Majorana type.