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# 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.

In SI units, permeability is measured in henries per metre, or newtons per ampere squared. The constant value μ0 is known as the magnetic constant or the permeability of vacuum, and has the exact or defined value μ0 = 4π×10−7 N·A−2.

## Relative permeability

Relative permeability, sometimes denoted by the symbol μr, 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: $\chi_m = \mu_r - 1 \,$

χm, a dimensionless quantity, is sometimes called volumetric or bulk susceptibility, to distinguish it from χp (magnetic mass or specific susceptibility) and χM (molar or molar mass susceptibility).

Magnetic permeability & susceptibility for selected materials
Medium Susceptibility Permeability x10-6
Mu-metal 20,000  25,000 N/A2 at 0.002 T
Permalloy 8000  10,000 N/A2 at 0.002 T
Transformer iron with ρ=0.01 µΩ·m 4000  5000 N/A2 at 0.002 T
Steel 700  875 N/A2 at 0.002 T
Nickel 100  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  1.2566650 N/A2
Hydrogen 8 × 10−9
or 2.2 × 10−9 
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 
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 μ0 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

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