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Magnetisation of a plain fluid

Can plain water, or the HHO off a cell, be magnetised by the coil — and how much?

The formula
M=χ⁢H,ΔB=μ0⁢M
M
Magnetisation, A/m
χ
Volume susceptibility
H
Applied field, A/m
ΔB
Added flux density, T
LaTeX 
M = χ \cdot H, \qquad ΔB = \mu_0 \cdot M

Work it out

The plain fluid or gas in the tube, with no particulate. Its own volume susceptibility is the whole answer.

kA/m

The drive coil's field in the tube. 50 kA/m is about 63 mT in air — a strong solenoid.

bar

For a gas, the density and with it the susceptibility scale with pressure; a liquid ignores this.

Compare with a variation

Result

M Magnetisation -0.452 A/m

The medium's magnetisation while it is in the field. Negative means it points against the field — a diamagnet.

χ Susceptibility -9.04e-6

The medium's volume susceptibility at this pressure. Of order 10⁻⁵ for a liquid and 10⁻⁶ or less for a gas at one atmosphere.

ΔB Added flux density -568 nT

μ₀M: what the medium adds to the flux density in the tube, over and above the coil's own μ₀H.

With your numbers
-0.452 A/m=-9.04e-6⁢50 kA/m,-568 nT=μ0⁢-0.452 A/m
LaTeX 
-0.452\,\mathrm{A/m} = -9.04e-6 \cdot 50\,\mathrm{kA/m}, \qquad -568\,\mathrm{nT} = \mu_0 \cdot -0.452\,\mathrm{A/m}

Worth knowing

  • Water is diamagnetic: its susceptibility is 9.04 parts per million and negative, so in the coil's field it magnetises against the field and is pushed very slightly out of it rather than drawn in. The magnetisation is -0.452 A/m, and a 5 % slurry of micron iron in this field carries about 16,600 times as much, the other way.
  • No remanence exists in a plain fluid or gas. A diamagnet or paramagnet is magnetised only while the field is on it; the instant the medium leaves the drive coil it is unmagnetised, and nothing is carried to a downstream coil. What a pickup coil would see from this medium is the drive coil's own field through the medium's parts-per-million, not anything the medium brought with it.

This result is a link — the address bar holds your numbers, so it can be pasted into a post and opened to the same answer.

What this looks like

Magnetisation against applied field Applied field swept from 25 kA/m to 75 kA/m with everything else held at your numbers. The dashed lines cross where you are.
Magnetisation against applied fieldMagnetisation falls from -0.226 A/m to -0.678 A/m as applied field rises from 25 kA/m to 75 kA/m. At your applied field of 50 kA/m it is -0.452 A/m.-0.7-0.6-0.5-0.4-0.3-0.22040608050 kA/m-0.452 A/mApplied field (kA/m)Magnetisation (A/m)
The formula behind the curve
M=χ⁢H,ΔB=μ0⁢M
M
Magnetisation, A/m
χ
Volume susceptibility
H
Applied field, A/m
ΔB
Added flux density, T
LaTeX 
M = χ \cdot H, \qquad ΔB = \mu_0 \cdot M
What moves the answer Each input moved 10% either way, with the others held still, and the effect on magnetisation.
What moves the answerMagnetisation is most sensitive to Applied field, which moves it by about 10% for a 10% change. It is least sensitive to Pressure, at about 0%.Change in the answer when each input moves by 10%-20%-10%10%20%Applied field±10Pressure±0
The formula behind the curve
M=χ⁢H,ΔB=μ0⁢M
M
Magnetisation, A/m
χ
Volume susceptibility
H
Applied field, A/m
ΔB
Added flux density, T
LaTeX 
M = χ \cdot H, \qquad ΔB = \mu_0 \cdot M

Method

  1. Look up the medium's volume susceptibility at 20 °C and one atmosphere: −9.0 × 10⁻⁶ for water, +1.8 × 10⁻⁶ for oxygen, +6.0 × 10⁻⁷ for the two-to-one hydrogen–oxygen mix off a cell, −2 × 10⁻⁹ for hydrogen alone.
  2. For a gas, scale the susceptibility with the pressure in atmospheres: twice the pressure is twice the molecules and twice the response. A liquid's density barely changes with pressure and its susceptibility is taken as fixed.
  3. Multiply by the applied field for the magnetisation, in amperes per metre — the same unit as the field, so the susceptibility is simply the ratio.
  4. Multiply by μ₀ for what the medium adds to the flux density. Against the coil's own μ₀H it is the susceptibility again: parts per million.
  5. Compare with a 5 % slurry of micron iron in the same field, which is demagnetisation-limited to about 0.15 H — the ratio is what "plain water" costs.

Assumptions

  • Linear response, M = χH, which holds for every diamagnet and for a paramagnetic gas at any field a coil can make: oxygen at room temperature is nowhere near saturating below hundreds of tesla.
  • Handbook susceptibilities at 20 °C. A paramagnet's falls as 1/T (Curie's law) and a diamagnet's does not change; neither moves enough to matter here.
  • A gas at pressure is an ideal gas: density and susceptibility proportional to pressure. Good to a per cent or so up to tens of bar.
  • No particulate at all. The moment any iron is in the tube this page is the wrong one, and the medium-susceptibility calculation is the right one; the two differ by four orders of magnitude at 5 % loading.
  • Nothing here is Meyer's. The estate material describes a medium in a tube and does not say what it is; the question "could it just be water, or the gas off the cell" is the archive's, and this is the arithmetic that answers it.