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Medium remanence and coercivity

What magnetisation does the medium keep after it leaves the coil?

The formula
Mr=φ⁢Mrp
Mr
Medium remanence, A/m
φ
Volume fraction of particulate, %
Mrp
Per-particle remanence: Ms ÷ 2 single-domain, min(Ms, 3·Hc) multi-domain, A/m
LaTeX 
Mr = φ \cdot Mrp

Work it out

The magnetic solid. Its coercivity is what decides everything on this page.

%

The solid's share of the volume. The medium keeps this fraction of what each particle keeps.

µm

Below the material's single-domain limit the particle keeps half its saturation; above it, only what its coercivity can hold against its own demagnetising field.

or see a worked example with typical numbers

Method

  1. Compare the particle diameter with the material's single-domain limit.
  2. Single-domain: an assembly of uniaxial particles with easy axes in every direction keeps half its saturation when the field is removed — the Stoner–Wohlfarth result. The per-particle remanence is Ms ÷ 2 and the coercivity is the material's.
  3. Multi-domain: a sphere's self-demagnetising field is a third of its magnetisation, and with no applied field to oppose it the domain walls move back until that field is no larger than the coercivity. The remanence is therefore about 3·Hc, capped at Ms for a material hard enough that the cap is never reached.
  4. Multiply the per-particle figure by the volume fraction for the medium's remanence, and divide by φ·Ms for the remanence ratio.

Assumptions

  • The Stoner–Wohlfarth half applies to non-interacting uniaxial single-domain particles with randomly oriented easy axes and no thermal relaxation — a blocked assembly. Superparamagnetic particles, those whose Néel time is shorter than the transit, keep nothing at all; the relaxation calculation decides which a given particle is.
  • The multi-domain figure is a demagnetisation argument, not a hysteresis measurement: it puts the sphere's remanent state where its internal field equals the coercivity, and takes N_d = 1/3 for a sphere. It is right to within a factor of two or so for soft materials and is generous for hard ones, where the cap at Ms is doing the work.
  • Coercivities of powders span an order of magnitude with grade, purity and grain size; the values here are mid-range for a commercial powder. Carbonyl iron in particular runs from a few tens to a few hundred amperes per metre.
  • No field in the tube after the coil. A stray field of the order of the coercivity, from the drive coil's fringe or a neighbouring magnet, reorganises a soft particulate's remanence entirely.
  • Nothing here is Meyer's. The estate material names the medium's speed and not its particulate; the calculation exists because a soft iron slurry and a hard ferrite slurry give opposite answers to whether a magnetised slug survives the trip to a pickup coil, and the archive can say which is which without a holding to cite.