# Permeability

The permeability ($\mu$) of a material, therefore, is a measure of the ease with which magnetic flux lines can be established in the material.
If cores of different materials with the same physical dimensions are used in the electromagnet described in previous section, the strength of the magnet will vary in accordance with the core used. This variation in strength is due to the greater or lesser number of flux lines passing through the core. Materials in which flux lines can readily be set up are said to be magnetic and to have high permeability.
It is similar in many respects to conductivity in electric circuits. The permeability of free space $\mu_o$ (vacuum) is $$\mu_o = 4\pi \times10^{-7} \, \text{Wb/A.m}$$ As indicated above, $\mu$ has the units of $Wb/A.m$. The SI unit of permeability is Henry/meter (H/m).
Practically speaking, the permeability of all nonmagnetic materials, such as copper, aluminum, wood, glass, and air, is the same as that for free space. Materials that have permeabilities slightly less than that of free space are said to be diamagnetic, and those with permeabilities slightly greater than that of free space are said to be paramagnetic. Magnetic materials, such as iron, nickel, steel, cobalt, and alloys of these metals, have permeabilities hundreds and even thousands of times that of free space. Materials with these very high permeabilities are referred to as ferromagnetic.

### Relative permeability

The ratio of the permeability of a material to that of free space is called its relative permeability; that is, $$\bbox[10px,border:1px solid grey]{\mu_r = { \mu \over \mu_o}}$$ In general, for ferromagnetic materials, $\mu_r \geq 100$, and for nonmagnetic materials, $\mu_r = 1$.