# Encyclopedia Magnetica™

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absolute_magnetic_permeability

# Absolute magnetic permeability

 Stan Zurek, Absolute magnetic permeability, Encyclopedia Magnetica, http://www.e-magnetica.pl/doku.php/absolute_magnetic_permeability

Absolute magnetic permeability $μ$ - a value of magnetic permeability of a given material, expressed in the units of henry per metre (H/m), rather than the unitless ratio to the permeability of vacuum $μ_0$. Typically, absolute permeability is referred to by the symbol $μ$ without any additional subscript.1)

Absolute permeability of vacuum is $μ_0$ = 4·π·10-7 H/m and encompasses the relationship between the magnetic flux density B and magnetic field strength H in vacuum, such that:

 (in vacuum) $$B = μ_0 · H$$ (T) ≡ (H/m)·(A/m)

In general, materials have permeability different from vacuum so that $μ_{material} \neq μ_0$, thus:

with absolute permeability
$$B = μ_{material} · H = μ · H$$ (T)
where: $μ_{material} = μ$ (H/m)

However, manipulating absolute values (in H/m) is more difficult in practice, because of the very small numbers for most magnetic materials. For example, if a magnetic material has the absolute permeability 1000 times greater than vacuum then its value would be just 0.001257 H/m, which is somewhat more difficult to directly apply.

For this reason, it is easier to use the value of relative permeability $μ_r$ as the figure of merit. By definition, the relative value is the ratio of the absolute value to the value in vacuum:2)

Relative permeability
$$\mu_r = \frac{\mu_{material}}{\mu_0} = \frac{\mu}{\mu_0}$$ (unitless)
where: $\mu_{material} = \mu$ - absolute permeability of material (H/m), $\mu_0$ - absolute permeability of vacuum (H/m)

Then, for the example of the absolute permeability being 1000 times greater, it can be simply stated that $\mu_r$ = 1000 (unitless), and typically the equation of relationship between B and H is written as:3)

with relative permeability
$$B = \mu_{material} · H = \mu_r · \mu_0 · H$$ (T)

Absolute permeability is a scalar and it is useful for analysing magnetic circuits which can be represented by a one-dimensional problem, i.e. such that the anisotropy of the material or shape can be neglected.

However, in certain cases also the permeability can be expressed with two orthogonal values, e.g. μr,x and μr,y, which approximate anisotropy with an elliptical function. This approach is used for example in some finite-element modelling software.4)

For full vector analysis, apart from B and H, also either the magnetisation M or magnetic polarisation J need to be taken into account.5)

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