# Absolute and Relative Magnetic Permeability

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Permeability is the measure of the ease, with which magnetic lines of force pass through a given material.

The ability of a material to concentrate magnetic flux is called permeability and its symbol is the Greek lower case letter μ. Any material that is easily magnetized tends to concentrate magnetic flux.

Because soft iron is easily magnetized, so it has a high permeability. The permeability of a material is a measure of how easy it is for flux lines to pass through it. Numerical values of μ for different materials are assigned by comparing their permeability with the permeability of air or vacuum.

Since soft iron has a high permeability (several hundred times that of air) it is much easier for magnetic flux to be conducted through it. The typical value of μ for iron vary from as low as 100 to as high as 5000, depending on the grade (quantity) used. The permeability of magnetic materials also varies according to the degree of magnetization.

## Magnetic Permeability Formula

Mathematically μ can be defined as the ratio of flux density to magnetizing force

$\mu =\frac{B~\left( Tesla \right)}{H~\left( {}^{A-t}/{}_{m} \right)}~~~~~\text{ }\cdots \text{ }~~~~~\left( 1 \right)$

## Absolute Permeability

The permeability of free space, μo, is

${{\mu }_{o}}=4\pi *~{{10}^{-7}}~{}^{H}/{}_{m}$

and is constant. The absolute permeability of another material can be expressed relative to the permeability of free space. Then,

$\mu ={{\mu }_{o}}{{\mu }_{r}}$

Where  is the dimensionless quantity called relative permeability.

## Relative Permeability

The relative permeability of a magnetic material, designated μr , is the ratio of its absolute permeability μ to that of air μo .

The μr of a nonmagnetic material such as air, copper, wood glass and plastic is, for all practical purposes, equal to unity. On the other hand, the μr of magnetic materials such as cobalt, nickel, iron, steel and their alloys are far greater than unity and are not constant.

Example

Calculate the absolute value of μ for a magnetic material whose μr is 800.

Solution

${{\mu }_{r}}=\frac{\mu }{{{\mu }_{0}}}$

From above equation, we have

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

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

If the field intensity and permeability of a circuit are known, we can calculate the flux density B using equation 1.

$\mu =\frac{B}{H}$

$B=\mu H$

From above equation, flux density can be calculated and expressed in Tesla.