What is Domains and hysteresis? — Physics

Definition 22.8 University Physics — Year 3 · Chapter 22 — Electromagnetism in Matter

A raw lump of iron is not magnetised: it shatters into domains, micron-scale regions each fully magnetised but pointing differently, so the exterior field (and its energy cost) nearly cancels. An applied $\vect H$ moves the domain walls — favourable domains grow — and then rotates whole domains into line. Walls snag on defects, so the process is irreversible: sweep $H$ up and down and $B(H)$ traces a loop, the hysteresis cycle. Switch the current off and a remanent field $B_{\text{r}}$ survives; cancelling it needs the reverse coercive field $H_{\text{c}}$ . The loop’s enclosed area is energy dissipated per cycle and per unit volume. Soft materials (silicon steel, ferrites: thin loop, small $H_{\text{c}}$ ) make transformer and motor cores; hard ones (alnico, Nd $_2$ Fe $_{14}$ B: fat loop, huge $H_{\text{c}}$ ) make permanent magnets — and magnetic memory: the refrigerator magnet and the hard disk are hysteresis loops that refuse to forget.

Domains. Left: a virgin ferromagnet hides its magnetisation in mutually cancelling regions. Right: the applied field grows and rotates them into a single magnetised block — through irreversible wall jumps that give iron its memory.

The hysteresis cycle. From the virgin state (dashed), the field drives B to saturation; returning H to zero leaves the remanence B_ r, and only the coercive field -H_ c erases it. Loop area = heat per cycle per unit volume: thin loops for transformers, fat loops for permanent magnets. — The hysteresis cycle. From the virgin state (dashed), the field drives $B$ to saturation; returning $H$ to zero leaves the remanence $B_{\text{r}}$ , and only the coercive field $-H_{\text{c}}$ erases it. Loop area = heat per cycle per unit volume: thin loops for transformers, fat loops for permanent magnets.

Examples

Example 22.9 (The iron-core electromagnet)

Wind $N$ turns carrying $I$ around an iron ring ( $\mu_{\text{r}} \sim 5000$ ) with a small air gap $e$ . Ampère’s law for $\vect H$ around the loop: $H_{\text{iron}}\ell + H_{\text{gap}}e = NI$ , and flux continuity makes $B$ common, so

B\Big(\frac{\ell}{\mu_0\mu_{\text{r}}} + \frac{e}{\mu_0}\Big) = NI .

With $\ell = 1\,\mathrm{m}$ and $e = 1\,\mathrm{cm}$ , the gap term is fifty times the iron term: nearly all the coil’s effort is spent pushing field across one centimetre of air. That is the magnetic circuit in one line — iron is a near-perfect conductor of flux, air the resistor — and it is why motors, relays and scrapyard lifters keep their air gaps ruthlessly thin (Problem 22.1).

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