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

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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.
 

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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?
Sure. The wire has its own magnetic field, too, giving a force on the source of the magnetic field.

Can you draw a sketch of your proposed setup?
 
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I apologize, I can't attach a drawing. Imagine a large amount of rectangular, current carrying loops wrapped around an axle much like a slinky wrapped around a rod with magnets fixed to the outside of the loops. The current carrying loops would all have current flowing in the same direction and all magnets having the same poles facing inward (lets say north facing inward). Would this still function as a motor, or would the force of the current carrying wire be canceled out by a force on the magnets in the opposite direction?
 

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