The permeability of a material is defined as the ease with which a flux can be created in that material. If there is no material, such as in a vacuum, the value can be shown to be 4E – 7π (or 4πE – 7; if you prefer). That is the permeability of free space (a vacuum), which has the abbreviation µ_{o}.

The permeability of free space is the reference against which the permeability of other materials is compared.

**Relative Permeability**

To compare the permeability of any given material with the permeability of free space, it is necessary to use a ratio µ_{r} which is known as the relative permeability of the material. For air and other non-magnetic materials, µ_{r} has the value of unity (µ_{r} = 1).

\[{{\mu }_{r}}=\frac{\mu }{{{\mu }_{o}}}\]

If the non-magnetic core of a solenoid is replaced with a magnetic material, the flux produced by the same number of ampere-turns may be greatly increased. The ratio of the flux produced by the magnetic core to that produced by the non-magnetic core is a direct result of the relative permeability of the magnetic material. For some magnetic materials µ_{r} can have a value in the thousands.

For any one magnetic material, the relative permeability value can vary considerably, being dependent on the flux density in the material. Relative permeability is higher at low values of **flux density**.

**Absolute Permeability**

To find the absolute permeability of a material, the permeability of free space is multiplied by the relative permeability of the material:

\[\mu ={{\mu }_{o}}{{\mu }_{r}}\]

**Where:**

**µ =**absolute permeability**µ**permeability of free space_{o}=**µ**relative permeability_{r}=

**Example**

Calculate the absolute permeability for a magnetic material whose μ_{r} is 800.

**Solution**

\[{{\mu }_{r}}=\frac{\mu }{{{\mu }_{0}}}\]

From above equation, we have

\[\mu ={{\mu }_{0}}{{\mu }_{r}}=800*4\pi *~{{10}^{-7}}\]

\[\mu =3200\pi *~{{10}^{-7}}~{}^{H}/{}_{m}\]