Does a current carrying wire attached to a magnet generate a force?

I have a bit of a theoretical question. If one has a current carrying wire in a magnetic field such as in an electric motor rotor, does the resulting force on the wire also impart an opposing force on the stator magnets which are producing the magnetic field as Newton’s third law says? Also, if one were to instead attach the magnets directly to the outside of the rotor instead of to the stator so that the current carrying wires are stationary relative to the magnets, would the resulting system still function and rotate the rotor as a normal motor or would any opposing forces in this system cancel each other out resulting in no rotation?

Thank you.