Magnet, wire and Newtons third law

[Zaigon]

I have been thinking about a bar magnet and an infinite wire in free space. The wire is positioned below the north pole of magnet and carries a current.

1) The force from the magent on the wire: Due to the magnetic field, the Lorentz force on the electrons in the wire creates a force on the wire which is directed perpendicular to the plan containing the wire and the magnet.

2) The force from the wire on the magnet: The magnetic field from the wire creates a torque on the magnet which tends to make it rotate, but is there any net force on the maget? What about Newtons third law here?

Will the magnet be accelerated in the opposite direction of the acceleration of the wire? And why?

 

[Dadface]

The third law gives a simple answer to this question which is that the force on the magnet is equal and opposite to that on the wire.

 

[Zaigon]

That I get, but I was interested in an explanation of this force.

In the meantime I have figured out how to explain it: The energy of the magnet in the magnetic field from the current is the dot product of the magnetic moment with the magnetic field. And this quantity depends on the horizontal position of the magnet (transverse to the wire), so the force (as the gradient of the energy) points in this direction, opposite to the force that the wire feels.