# 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 September of 1885, Oliver Heaviside coined this term.

In SI units, permeability is measured in henrys per metre. The constant value [itex]\mu_0 \,[itex] 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:
[itex] \mathbf{M}=\chi_m\mathbf{H}[itex]
Where [itex]\chi_m \,[itex] is a dimensionless scalar called the magnetic susceptibility.
According to the definition of the auxiliary field, [itex]\mathbf{H}[itex]

[itex]\mathbf{B}=\mu_0 (\mathbf{H}+\mathbf{M})=\mu_0 (1 + \chi_m)\mathbf{H}[itex]

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

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

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## 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 [itex]\varepsilon_0\mu_0 = \frac{1}{c^2}[itex]

## 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:

[itex]\mu_{r} = \frac{\mu}{\mu_{0}} [itex]

## Magnetic susceptability

Magnetic susceptibility is defined as:

[itex]\chi_m = \mu_r - 1 \,[itex]

## Some values for magnetic permeability and magnetic susceptability

Magnetic permeability & susceptibility for some materials
Medium [itex]\chi_m = \mu_r - 1 \,[itex] [itex] \mu \,[itex]
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
Aluminum 22.2 × 10-6 1.2566650 µN/A2
Platinum 265 × 10-6 1.2569701 µN/A2

## SI magnetism units

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