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Physics · পরিভাষা

Domains and hysteresis কী?

Definition 22.8 University Physics — Year 3 · অধ্যায় 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 H→\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 HH up and down and B(H)B(H) traces a loop, the hysteresis cycle. Switch the current off and a remanent field BrB_{\text{r}} survives; cancelling it needs the reverse coercive field HcH_{\text{c}}. The loop’s enclosed area is energy dissipated per cycle and per unit volume. Soft materials (silicon steel, ferrites: thin loop, small HcH_{\text{c}}) make transformer and motor cores; hard ones (alnico, Nd2_2Fe14_{14}B: fat loop, huge HcH_{\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.
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 BB to saturation; returning HH to zero leaves the remanence BrB_{\text{r}}, and only the coercive field −Hc-H_{\text{c}} erases it. Loop area = heat per cycle per unit volume: thin loops for transformers, fat loops for permanent magnets.

উদাহরণ

Example 22.9 (The iron-core electromagnet)

Wind NN turns carrying II around an iron ring (μr∼5000\mu_{\text{r}} \sim 5000) with a small air gap ee. Ampère’s law for H→\vect H around the loop: Hironℓ+Hgape=NIH_{\text{iron}}\ell + H_{\text{gap}}e = NI, and flux continuity makes BB common, so

B(ℓμ0μr+eμ0)=NI.B\Big(\frac{\ell}{\mu_0\mu_{\text{r}}} + \frac{e}{\mu_0}\Big) = NI .

With ℓ=1 m\ell = 1\,\mathrm{m} and e=1 cme = 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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