Why magnets attract or repel each other

[hushai1]

I would like to understand at a microscopic level why magnets attract or repel each other. I understand that there are tiny loops of currents caused by the spin and orbital rotations of electrons, that there are magnetic moments, but I don't understand why magnets attract. How is the magnetic force (F=qv x B) acting? What is doing the work since magnetic forces are not doing any work? Thank you

 

[Bill_K]

Consider one of the magnets (1) to be a tiny current loop, and ask how it will be influenced by the magnetic field of the other magnet (2). The force on each moving charge in the current loop is e v x B. At opposite sides of the loop the v's are equal and opposite, so in a uniform B field the force averages out to zero.

But near the pole of magnet 2 the B field is not uniform. Near the North pole the lines of B will be diverging, while near the South pole they will be converging. That means the circular loop does not just see a B field perpendicular to its plane, it also sees an additional radial component to the B field pointing outward (or inward). Since v is tangential and B is radial, v x B will be perpendicular to the plane of the loop, and the loop will be attracted (or repelled).

 

[hushai1]

Thank you for your answer. I think it is a good answer. I don't understand however, why, if magnetic forces don't work, there is still some work done since one magnet is able to attract another magnet. Thank you.