Permeability

In electromagnetism, permeability is a material property that measures the flux density (per unit area, the magnetisation). We represent with a $\mu$, in units of Henries per metre ($H/m$) or equivalently newtons per ampere squared ($N/A^2$).

The permeability of free space (also the permeability constant or magnetic constant) quantifies the strength of the magnetic field emitted by a current in a vacuum. It’s defined by:¹

$${\mu }_0=4\pi \times 10^{-7}H\cdot m^{-1}=1.25637\times 10^{-6}N\cdot A^{-2}$$

We can express the permeability of a material with $\mu ={\mu }_r{\mu }_0$, where ${\mu }_r$ is the relative permeability of the material. This results in an expression:

$$\vec{B}={\mu }_0{\mu }_r\vec{H}$$

The relative permeability can also be expressed as:

$${\mu }_r=\frac{\mu }{{\mu }_0}=1+{\chi }_m$$

where ${\chi }_m$ is the magnetic susceptibility.

Footnotes

1. Not anymore since 2019. The exact SI definition is the same up to the 8th decimal digit. ↩