Relative Permeability

In this topic, you study Relative Permeability.

In a solenoid, if the core of iron or any other ferromagnetic material is introduced (See Fig. 1) in the place of air or a former of non-magnetic material, the flux inside the coil is intensified. It means that for the same value of magnetic field strength (H), the flux density (B) is increased.

Fig. 1: Relative Permeability.

The ratio of the flux density produced in a material to the flux density produced in a vacuum (or free space) by the same magnetic field strength under identical conditions is called the relative permeability (μr) of that material.

If B is the flux density (in tesla) produced in a particular material by a certain value of H and B₀ the flux density in tesla) produced in a vacuum by the same value of H under identical conditions, then by definition,

Relative permeability,

\[{{\text{ }\!\!\mu\!\!\text{ }}_{\text{r}}}=\text{ }\frac{\text{B}}{{{\text{B}}_{\text{0}}}}\]

We know that

\[{{\text{B}}_{\text{0}}}=\text{ }{{\text{ }\!\!\mu\!\!\text{ }}_{0}}\text{ H}\]

and

\[\text{B}=\text{  }\!\!\mu\!\!\text{  H}\]

∴

\[{{\text{ }\!\!\mu\!\!\text{ }}_{\text{r}}}=\text{ }\frac{\text{B}}{{{\text{B}}_{\text{0}}}}\text{ }=\text{ }\frac{\text{ }\!\!\mu\!\!\text{  H}}{{{\text{ }\!\!\mu\!\!\text{ }}_{0}}\text{ H}}\text{ }=\text{ }\frac{\text{ }\!\!\mu\!\!\text{  }}{{{\text{ }\!\!\mu\!\!\text{ }}_{0}}}  …(1)\]

or,

\[\text{ }\!\!\mu\!\!\text{ }=\text{ }{{\text{ }\!\!\mu\!\!\text{ }}_{0}}\text{ }{{\text{ }\!\!\mu\!\!\text{ }}_{\text{r}}}\]

From the Expression (1), it is obvious that the relative permeability of the material is nothing but its absolute permeability stated as relative to the permeability of free space. It being a ratio of absolute permeability to permeability of free space, has no unit. For air and non-magnetic materials, since $\text{ }\!\!\mu\!\!\text{ }=\text{ }{{\text{ }\!\!\mu\!\!\text{ }}_{0}}\text{ }{{\text{ }\!\!\mu\!\!\text{ }}_{\text{r}}}$

Relative permeability,

\[{{\text{ }\!\!\mu\!\!\text{ }}_{\text{r}}}=\text{ }1\text{ }\]

On the other hand, for certain metals like nickel-iron alloys, it may be as high as 100,000. If the maximum flux is the main requirement, then clearly the value of the relative permeability is a measure of the suitability of the material chosen for the core. The higher the value of the relative permeability, better will be the material for such conditions.