I was pondering this question as to why magnetic circuits conduct magnetic field lines in Fall 2017.
This is a progress report (rough idea), I have not peer reviewed these ideas nor completed the calculations.
I plan to invest more work (and program some real graphs) if the question keeps coming up in my researches,
or if this post generates interest from the community. If the dear reader have any feedback, suggestions, or questions, feel free to comment.
The claim is simply that the south of the magnetic dipoles in the circuit have a statistical tendency to point towards the north of nearby dipoles.
A magnetic field line passing through the circuit will tend to (probabilistically) polarize the dipoles. We have the Bohr megneton:
We also have the energies of non-interacting spins of electrons (spin up or spin down) (Where B denotes the magnetic field strength):
Next, we have that the applied magnetic field B has Boltzmann statistics (and tau=k_B T is the temperature in Boltzmann units) on alligned spins:
This indicates that the probability of the spin aligning is more than the probability of anti-aligning.
Each dipole moment then goes on to generate a magnetic field of its own, which dominates nearby dipoles:
This is how magnetic circuits can round-corners:
Another question that has been occupying my thoughts at night is: does B_applied constitute an observer?
The magnetization density will depend on the metal. See also: the Pauli exclusion principle. Also, in paramagnetic materials orbitals occupied with odd numbers of electrons can easily change spin. In diamagnetic materials, filled orbitals resist magnetic flux.