  We show that the He-McKellar-Wilkens effect can induce a persistent flow in a
Bose-Einstein condensate of polar molecules confined in a toroidal trap, with
the dipolar interaction mediated via an electric dipole moment. For
Bose-Einstein condensates of atoms with a magnetic dipole moment, we show that
although it is theoretically possible to induce persistent flow via the
Aharonov-Casher effect, the strength of electric field required is prohibitive.
We also outline an experimental geometry tailored specifically for observing
the He-McKellar-Wilkens effect in toroidally-trapped condensates.
