What is Magnetisation, bound currents, and H?

The magnetic story runs in parallel. Matter is full of microscopic current loops — orbiting and spinning electrons, each a magnetic dipole $\vect\mu$; their density is the magnetisation $\vect M = n\langle\vect\mu\rangle$. A uniformly magnetised block is equivalent to a bound surface current circulating around its sides (interior loops cancel pairwise; a bar magnet is a solenoid of bound current). Splitting currents into free and bound, Ampère’s law rearranges around the auxiliary field

$\vect H$ is sourced by the currents in our wires (units $\mathrm{A}/\mathrm{m}$), while $\vect B$ keeps the physics — forces, flux, induction. Linear media have $\vect M = \chi_{\text{m}}\vect H$ and $\vect B = \mu_0(1 + \chi_{\text{m}})\vect H = \mu_0\mu_{\text{r}}\vect H$.