# Absolute and Relative Magnetic Permeability (µ)

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## Absolute Magnetic Permeability

The absolute (or actual) magnetic permeability of a material is its conductivity for the magnetic flux. It is denoted by a Greek letter μ ‘(mu)’ and measured in Henry per meters (H/m). Thus,

Absolute permeability of material,

$$\mu=\mu_{0}\mu_{r}\:H/m$$

Where,

• μ0 = absolute permeability of air or vacuum.

• μr = relative permeability of the material.

The higher the permeability of a magnetic material, the greater its conductivity for magnetic flux and vice-versa.

Air or vacuum is the poorest conductor of the magnetic flux. The absolute magnetic permeability of the air is μ0 = 4π × 10−7 H/m . The absolute permeability (μ) of a magnetic material is very high as compared to permeability of air or vacuum 0).

Note − The absolute magnetic permeability of all the non-magnetic materials is also 4π × 10−7 H/m .

## Relative Magnetic Permeability

The relative magnetic permeability of a magnetic material is the measure of relative ease with which that magnetic material conducts magnetic flux as compared with the conduction of magnetic flux in air.

Quantitatively, the relative permeability is given by the ratio of absolute permeability (μ) of magnetic material to the absolute permeability (μ0) of air or vacuum and is denoted by μr, i.e.

Relative magnetic permeability,

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

The relative magnetic permeability is a dimensionless quantity i.e. it does not have unit, because it is the ratio of two quantities of same dimensions.

Now, for air or vacuum, μ = μ0, therefore,

$$\mu_{r(air)}=\frac{\mu_{0}}{\mu_{0}}=1$$

Hence, the relative magnetic permeability of air or vacuum is 1.

However, the relative permeability for magnetic materials is very high (ex. pure iron has µr = 8000).

The cores of all electromagnetic devices (like transformers, generators, motors etc.) are made of magnetic materials, due to the high relative magnetic permeability.

## Numerical Example

A core of a transformer is made up of soft iron of relative permeability µr = 8000. Determine the absolute permeability of the core.

Solution −

Absolute permeability,

$$\mu=\mu_{0}\mu_{r}=(4\pi\times\:10^{-7})\times\:(8000)$$

$$\Rightarrow\:\mu=0.010048\:H/m=1.0048\times\:10^{-2}H/m$$

Here it can be seen that the absolute permeability of the soft iron is greater than that of the air or vacuum.

Published on 02-Jul-2021 08:23:13