Moving the magnetic field around a fixed conductor?
Yes, a magnet that is moving such that it creates a current in a non-moving wire will feel a force resisting that motion.

You can make a generator with spinning magnets instead of spinning wires like this one...



As the magnets move, they induce a current in the wire. The induced current itself make a magnet field on the opposite direction, opposes the rotation of the magnets. 

Keep in mind that the lines of magnetic force must be cutting though the wire to induce a current in it, so just rotating a magnet around a wire such that one of its poles is always pointing toward the wire will not induce a current, and therefore will not create a back force. 

Also keep in mind that it is the current flowing in the wire that creates the field that creates the back force, so the wire must be in a circuit or else no force. You can demonstrate this by spinning an unconnected stepper motor with your fingers, and then shorting the wires and spinning it again. It is harder to turn when the wires are shorted. Most stepper motors have fixed coils and turning magnets btw.

If you are interested in electromagnetics, I'd highly recommend this book...



Electricity and Magnetism 3rd Edition
by Edward M. Purcell

Yo can find a free PDF version on google.