  The artificial magnetic fields engineered for ultra cold gases depend on the
internal structure of the neutral atoms. Therefore the components of a mixture
composed of two atomic gases can exhibit a different response to an artificial
magnetic field. Such a mixture can be interpreted as a mixture of two atomic
gases, carrying different synthetic charges. In this article, we consider such
mixtures of two superfluids with unequal synthetic charges in a ring trap
subject to a uniform artificial magnetic field. The charge imbalance in such a
mixture changes the distribution of excited particles over angular momentum
states compared to that of an equally charged mixture. This microscopic
difference exhibits macroscopic consequences; such as the occurrence of an
angular momentum transfer between two unequally charged components. Due to the
inter-fluid atomic interactions in a ring, the angular momentum transfer can
create a counter flowing persistent current in the weakly charged superfluid.
Even in the limiting case of a charged and an uncharged superfluid mixture, a
persistent current can be induced in the uncharged superfluid, despite the fact
that it is not directly coupled to the magnetic field. The stability analysis
shows that the induction depends on the interplay between inter-fluid
interaction and the applied magnetic field. We obtain instability boundaries of
the system and construct phase diagrams as a function of the inter-fluid
interaction and the magnetic field. We investigate these properties employing
the Bogoliubov approximation.
