 # Magnetic Permeability

Magnetic permeability also referred to as just permeability in electromagnetism is a property of a magnetic material which supports the formation of a magnetic field. This property basically allows the magnetic lines of force to pass through the material.

In other words, the magnetic permeability of a material can also be said to be its magnetization capability. This helps in determining how much of magnetic flux that a material can support to pass through it.

## What is Magnetic Permeability?

Magnetic permeability is defined as the ratio of the magnetic induction to the magnetic intensity. It is a scalar quantity and denoted by the symbol μ. It is measured in units such as Weber per ampere meter or Henry meter or Newton per ampere square.

Magnetic permeability helps us measure a material’s resistance to the magnetic field or measure of the degree to which magnetic field can penetrate through a material. If the material has greater magnetic permeability, greater will be the conductivity for magnetic lines of force.

Permeability also depends on several factors such as the nature of the material, humidity, position in the medium, temperature, and frequency of the applied force. Magnetic permeability is always positive.

## Magnetic Permeability Formula

Magnetic permeability (u) = B/H

Magnetic permeability = (magnetic intensity) / (magnetising field)

## Types of Permeability

Permeability of Free Space

Also known as the permeability of free space, air or vacuum.

It is represented by u0=B0/H

The ratio of magnetic intensity in a vacuum and magnetising field.

Permeability of Medium

It is expressed as;

u = B/H

The ratio of magnetic intensity in the medium and magnetising field.

Relative Permeability

Its expression is given as;

ur = u/um

Relative permeability = (number of lines of magnetic induction per unit area in a material)/(number of lines per unit area in a vacuum)

Relative permeability is a dimensionless quantity, It is the ratio of two quantities with the same units, so relative permeability has no unit. Relative permeability of free space is 1.

## Magnetic Permeability Materials

Materials may be classified on the basis of their permeability as;

### Diamagnetic materials

Diamagnetic materials have a constant relative permeability slightly less than 1, that’s why magnetic flux density inside diamagnetic materials is slightly reduced. Diamagnetic materials are feebly repelled in external magnetic fields.

Example: Bismuth

### Paramagnetic Materials

Paramagnetic materials have a constant relative permeability slightly greater than 1, that’s why when a paramagnetic material placed in an external field it gets feebly magnetized in the direction of the magnetic field.

Example: Platinum

### Ferromagnetic Materials

Ferromagnetic materials do not have constant relative permeability.

Pure iron and many alloys have relative permeability greater than 100000, as the magnetising field increases relative permeability increases. That’s why ferromagnet materials have the strongest magnetic properties.

Example: Iron

## Relation Between Relative Permeability and Magnetic Susceptibility

The relation between magnetic susceptibility and relative permeability is described as;

χm = μr − 1

Lets us understand how we can establish or derive this equation.

First, we take some relevant equations.

B = μo(H+M) and M=XmH

Substituting the values, we get;

B = μo(H+XmH)

B = μoH(1+Xm)

So,

μH = μoH(1+Xm)

μ/μo = μr

Xm=1 – μr