Permeability (electromagnetism)

In electromagnetism, permeability is the degree of magnetization of a material that responds linearly to an applied magnetic field. Magnetic permeability is represented by the Greek letter μ. The term was coined in September, 1885 by Oliver Heaviside.

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In SI units, permeability is measured in henries per metre, or newtons per ampere squared. The constant value $μ 0$ is known as the magnetic constant or the permeability of vacuum, and has the exact or defined value $μ 0$ = 4π×10⁻⁷ N·A⁻².

Relative permeability

Relative permeability, sometimes denoted by the symbol μ_r, is the ratio of the permeability of a specific medium to the permeability of free space μ₀:

$\mu_{r} = \frac{\mu}{\mu_{0}}$

In terms of relative permeability, the magnetic susceptibility is:

$\chi_m = \mu_r - 1 \,$

χ_m, a dimensionless quantity, is sometimes called volumetric or bulk susceptibility, to distinguish it from χ_p (magnetic mass or specific susceptibility) and χ_M (molar or molar mass susceptibility).

Magnetic permeability & susceptibility for selected materials
Medium	Susceptibility	Permeability x10^-6
Mu-metal	20,000 ^[1]	25,000 N/A²	at 0.002 T
Permalloy	8000 ^[1]	10,000 N/A²	at 0.002 T
Transformer iron with ρ=0.01 µΩ·m	4000 ^[1]	5000 N/A²	at 0.002 T
Steel	700 ^[1]	875 N/A²	at 0.002 T
Nickel	100 ^[1]	125 N/A²	at 0.002 T
soft ferrite with ρ=0.1 Ωm	source, ferroxcube	5000 N/A²	< 0.1 mT
soft ferrite with ρ=10 Ωm	source, ferroxcube	2500 N/A²	< 0.1 mT
Platinum	2.65 × 10⁻⁴	1.2569701 N/A²
Aluminum	2.22 × 10⁻⁵ ^[2]	1.2566650 N/A²
Hydrogen	8 × 10⁻⁹ or 2.2 × 10⁻⁹ ^[2]	1.2566371 N/A²
Vacuum	0	1.2566371 N/A²
Sapphire	−2.1 × 10⁻⁷	1.2566368 N/A²
Copper	−6.4 × 10⁻⁶ or −9.2 × 10⁻⁶ ^[2]	1.2566290 N/A²
Water	−8.0 × 10⁻⁶	1.2566270 N/A²

Permeability varies with magnetic field. Values shown above are approximate and valid only at the magnetic fields shown. Moreover, they are given for a zero frequency; in practice, the permeability is generally a function of the frequency. When frequency is considered the permeability can be complex, corresponding to the in phase and out of phase response.

Note that the magnetic permeability $μ 0$ has an exact value in SI units (i.e. there is no error bar or uncertainty in its value), because the definition of ampere fixes its value to 4π × 10⁻⁷ H/m exactly.

References

^ ^a ^b ^c ^d ^e "Relative Permeability", Hyperphysics
^ ^a ^b ^c Clarke, R. Magnetic properties of materials, surrey.ac.uk

Permeability (electromagnetism)

Additional recommended knowledge

Better weighing performance in 6 easy steps

Correct Test Weight Handling Guide: 12 Practical Tips

Guide to balance cleaning: 8 simple steps

Relative permeability

References

See also

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