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 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}}

Magnetic susceptibility is defined as:

\chi_m = \mu_r - 1 \,

colspan=3\|Magnetic susceptibility for some materials
tyle="background:#ffdead;" \| Medium	style="background:#ffdead;" \| $\chi_m = \mu_r - 1 \,$	style="background:#ffdead;" \| $\mu \,$
a href="/encyclopedia/Hydrogen" title="Hydrogen">Hydrogen	0.008 × 10^-6	1.2566371 µN/A²
a href="/encyclopedia/Copper" title="Copper">Copper	−6.4 × 10^-6	1.2566290 µN/A²
a href="/encyclopedia/Water" title="Water">Water	−8.0 × 10^-6	1.2566270 µN/A²
a href="/encyclopedia/Aluminium" title="Aluminium">Aluminium	22.2 × 10^-6	1.2566650 µN/A²
a href="/encyclopedia/Platinum" title="Platinum">Platinum	265 × 10^-6	1.2569701 µN/A²

SI magnetism units

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