  In this work we extend our previously developed formalism of Newtonian
multi-fluid hydrodynamics to allow for coupling between the fluids and the
electromagnetic and gravitational field. This is achieved within the convective
variational principle by using a standard minimal coupling prescription. In
addition to the conservation of total energy and momentum, we derive the
conservation of canonical vorticity and helicity, which generalize the
corresponding conserved quantities of uncharged fluids. We discuss the
application of this formalism to electrically conducting systems,
magnetohydrodynamics and superconductivity. The equations of electric
conductors derived here are more general than those found in the standard
description of such systems, in which the effect of entrainment is overlooked,
despite the fact that it will generally be present in any conducting
multi-constituent system.
