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# Permeability (electromagnetism)

In electromagnetism, permeability is the degree of magnetisation of a material that responds linearly to a magnetic field. Magnetic permeability is represented by the symbol μ. In SI units, permeability is measured in henrys per metre. The constant value $\mu_0 \,$ is known as the magnetic constant, or by the older term permeability of a vacuum (absolute permeability below).

Permeability in linear materials owes its existence to the approximation:
$\mathbf{M}=\chi_m\mathbf{H}$
Where $\chi_m \,$ is a dimensionless scalar called the magnetic susceptibility
According to the definition of the auxiliary field, $\mathbf{H}$

$\mathbf{B}=\mu_0 (\mathbf{H}+\mathbf{M})=\mu_0 (1 + \chi_m)\mathbf{H}$

$\mu=\mu_0(1+ \chi_m) \,$
Thus $\mu = \frac {B} {H} \,$

where

μ is the permeability, measured in henrys per metre

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

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

## Absolute permeability

Absolute permeability (the magnetic constant) is represented by the symbol μ0 and is the permeability of the vacuum, where μ0 = 4π×10−7 N A−2 (exactly).

The permittivity of free space (the electric constant) and the magnetic constant are related to the speed of light (c) by the formula $\varepsilon_0\mu_0 = \frac{1}{c^2}$

## 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:

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

Magnetic susceptibility is defined as:

$\chi_m = \mu_r - 1 \,$
Magnetic susceptibility for some materials
Medium $\chi_m = \mu_r - 1 \,$ $\mu \,$
Hydrogen 0.008 × 10-6 1.2566371 µN/A2
Copper −6.4 × 10-6 1.2566290 µN/A2
Water −8.0 × 10-6 1.2566270 µN/A2
Aluminium 22.2 × 10-6 1.2566650 µN/A2
Platinum 265 × 10-6 1.2569701 µN/A2

## SI magnetism units

03-10-2013 05:06:04