Force on moving mass from magnet and coil

I have two parts:

• The first part is fixed.
• The second part can move with respect to the first part.

A permanent magnet is attached to the first part and a coil is attached to the second part.

When there is current in the coil, Lorentz force is applied to the coil from the magnetic flux induced by the magnet, and the same amount of force is applied on the second part, causing it to move.

My question is: Will the magnetic permeability of the second part affect the force that moves it.

The permeability definitely changes the magnetic flux flowing through the coil. So the force applied to the coil must change.

From here I have two theories:

1. According to Newton's 3rd law, the "difference" in the magnetic flux generates a reaction force that is applied to the moving part itself (hence not moving it) and not to the fixed part, so the force stays the same - it is not affected by the magnetic permeability of the moving part.
2. The permeability only changes the direction of the magnetic flux. The magnetic flux is generated by the permanent magnet so the reaction force is applied to the permanent magnet, hence the force that moves the second part also changes with respect to the permeability of the moving part.

Does someone know which one is correct?