It helps here to be a bit more specific. Are you talking about an external magnetic field applied to a conducting loop?
Are you referring to a wire of current $I$ that creates a magnetic field $B$?
If you hook up a loop of wire with a potential $V$ so that it has a current $I$ and hence a magnetic field $B(I)$. You then you pull out the potential. The resistance in the circuit will slow down the charges, the current will dec. and the magnetic field will start to decrease as well.
What I think you are proposing would violate the conservation of energy. A B field being produced by a loop of wire needs an external source of energy to actually maintain that situation.
An external time-varying magnetic field would induce an emf and current in a loop of wire, but again, we're pumping energy into the system. Static magnetic fields on their own do not linearly accelerate charges (they do no work on a system) therefore they cannot be used as a power source directly.