Permeability (electromagnetism)

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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 symbol μ. This term was coined in September, 1885 by Oliver Heaviside.

In SI units, permeability is measured in henrys 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 value μ₀ = 4π×10⁻⁷ N/A².

Some materials, called ferromagnetic or ferromagnets, are highly magnetic by nature, relative to most materials. They are composed of a large number of very small magnetic units working together called domains. Domains are not always aligned, and they often act against each other to reduce the strength of the net magnetic field.

If one puts the ferromagnetic material into an externally applied magnetic field, the domains tend to line up, so that the sum of the fields from the ferromagnet and the applied magnetic field is higher in magnitude than the applied magnetic field alone.

Permeability in linear materials owes its existence to the approximation:

[ \mathbf=\chi_m\mathbf]

where [\chi_m \,] is a dimensionless scalar called the magnetic susceptibility.

According to the definition of the auxiliary field, H

[\mathbf=\mu_0 (\mathbf+\mathbf)=\mu_0 (1 + \chi_m)\mathbf = \mu \mathbf]

where

μ is the material's permeability, measured in henries per metre

B is the magnetic flux density (also called the magnetic induction) in the material, measured in teslas

H is the auxiliary field strength, measured in amperes per metre

M is the material's magnetization, measured in amperes per metre

The permittivity of free space (the electric constant) and the magnetic constant are related to the speed of light (c) by the formula: [\varepsilon_0\mu_0 = \frac]

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_ = \frac} ]

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
Mumetal 20,000 ["Relative Permeability", Hyperphysics] 25,000 µN/A² at 0.002 T
Permalloy 8000 ["Relative Permeability", Hyperphysics] 10,000 µN/A² at 0.002 T
Transformer iron 4000 ["Relative Permeability", Hyperphysics] 5000 µN/A² at 0.002 T
Steel 700 875 µN/A² at 0.002 T
Nickel 100 125 µN/A² at 0.002 T
Platinum 2.65 × 10⁻⁴ 1.2569701 µN/A²
Aluminum 2.22 × 10⁻⁵ [Clarke, R. Magnetic properties of materials, surrey.ac.uk] 1.2566650 µN/A²
Hydrogen 8 × 10⁻⁹
or 2.2 × 10 > 1.2566371 µN/A²
Vacuum 0 1.2566371 µN/A²
Sapphire −2.1 × 10⁻⁷ 1.2566368 µN/A²
Copper −6.4 × 10⁻⁶
or -9.2 × 10⁻⁶ 1.2566290 µN/A²
Water −8.0 × 10⁻⁶ 1.2566270 µN/A²

Magnetic permeability & susceptibility for selected materials
Medium	Susceptibility	Permeability
Mumetal	20,000 ["Relative Permeability", Hyperphysics]	25,000 µN/A²	at 0.002 T
Permalloy	8000 ["Relative Permeability", Hyperphysics]	10,000 µN/A²	at 0.002 T
Transformer iron	4000 ["Relative Permeability", Hyperphysics]	5000 µN/A²	at 0.002 T
Steel	700	875 µN/A²	at 0.002 T
Nickel	100	125 µN/A²	at 0.002 T
Platinum	2.65 × 10⁻⁴	1.2569701 µN/A²
Aluminum	2.22 × 10⁻⁵ [Clarke, R. Magnetic properties of materials, surrey.ac.uk]	1.2566650 µN/A²
Hydrogen	8 × 10⁻⁹ or 2.2 × 10 >	1.2566371 µN/A²
Vacuum	0	1.2566371 µN/A²
Sapphire	−2.1 × 10⁻⁷	1.2566368 µN/A²
Copper	−6.4 × 10⁻⁶ or -9.2 × 10⁻⁶	1.2566290 µN/A²
Water	−8.0 × 10⁻⁶	1.2566270 µN/A²

Permeability varies with flux density. Values shown are approximate and valid only at the flux densities shown.

Permeability (electromagnetism)

References

See also