### Table of Contents

# Absolute magnetic permeability

Stan Zurek, Absolute magnetic permeability, Encyclopedia Magnetica, https://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)}

^{S. Zurek, E-Magnetica.pl, CC-BY-4.0}

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. *μ _{r,x}* and

*μ*, which approximate anisotropy with an elliptical function. This approach is used for example in some finite-element modelling software.

_{r,y}^{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)}

→ → → Helpful page? Support us!→ → → | PayPal | ← ← ← Help us with just $0.10 per month? Come on… ← ← ← |

## See also

## References

^{2)}Bureau International des Poids et Mesures, The International System of Units (SI), 9th edition, 2019, {accessed 2021-04-10}

^{4)}David Meeker, Finite Element Method Magnetics: Documentation, {accessed 2021-06-25}