Relative permeability: why does $\mu_{air} = \mu_0$? I read here that the relative permeability of the air equals $\mu_0$, meaning that the reluctance of an air gap in a magnetic circuit equals the one of a vacuum gap. Yet, air and vacuum are significantly different... So why does $\mu_{air} = \mu_0$ ?
 A: Ferromagnetic materials can have large $\mu$. But for paramagnetic and diamagnetic materials, a typical permeability is
$
\mu_r = \frac{\mu}{\mu_0} ≈ 1 \pm 10^{-5}
$.
I don’t know of a good fundamental explanation for this. It may be related to the fact that magnetic transitions are generally weaker/slower than electric transitions which carry the same angular momentum. For example, an atomic or nuclear state which can decay by emitting either an electric dipole “E1” photon or a magnetic dipole “M1” photon, with similar energies, will mostly wind up the the daughter state corresponding to the electric transition.  But the conceptual leap from atomic or molecular states to the collective properties of materials is nontrivial and not my expertise, so I could be just spitballing.
Furthermore, air is a low-density material, so any collective effects (to the extent you can even have a collective phenomenon in a non-interacting ideal gas) will be much smaller than corresponding effects in condensed matter.
