What causes force between two poles of magnets on an atomic level?

Question

My textbook says that all magnetism can be linked to circulating current. In an atomic level, the magnetic fields are generated due to electrons revolving about their nuclei. Taking the case of a simple hydrogen atom placed in an external magnetic field $B_{ext}$.

The external magnetic field is into the plane of screen and so is the magnetic field produced by the atom. The external magnetic field can be thought of a South pole of a magnet behind the (hydrogen) atom. The magnetic field produced by the atom can be thought of a bar magnet with South Pole out of the screen. As north and south pole attract, the force due to external magnetic $F_{B_{ext}}$ field should be towards the magnet behind the atom. However the net force is perpendicular to that expected and if we take many atoms, the net force should be zero.

What went wrong here?

Answer 1

You just discovered that net force on a magnetic dipole in uniform magnetic field is zero. In order to have a net force you need a non-uniform field (a gradient of the field).

However your model with the hydrogen atom is not relevant from a different reason. The orbital motion of electrons produces a diamagnetic behavior. There are materials which are repelled by strong magnets and these are called diamagnetic materials. Part o this behavior can be explained based on the orbital "motion" of electrons.

However, the strong magnetism (ferromagnetism), like when iron is attracted by a magnet, is due to the spin magnetism of the electrons. This is an intrinsic properties of electrons and it is not due to electric currents. Mathematically the ferromagnetism can be described in terms of current densities but this is just a mathematical tool.