What happens when a coil of wire cuts through a magnetic field?

If the magnetic field is fluctuating, or the coil of wire and magnetic field are moving with respect to each other, then a current is induced in the coil of wire.

If the two are stationary and the magnetic field is stable, then no current is induced in the coil. However, if there is a current in the coil, from another source, then the coil and the field will exhibit a relative force that will tend to move the coil with respect to the field.