Magnetic Permeability (μ)

What is Magnetic Permeability(μ) ?

Definition: Magnetic Permeability is defined as the property of the material to allow the magnetic line of forces to pass through it.

In other words, Magnetic Permeability is the ability of material to support the development of magnetic field.

Hence, The Magnetic Permeability is the degree of magnetization capability that a material obtains in response to an external applied magnetic field.

So, in electromagnetism we can say that Permeability is the measure of resistance of a material against the formation of a magnetic field.

If the magnetic permeability of a magnetic material is higher, then the conductivity of the material will also be higher.

         Table of Contents

1. What is Magnetic Permeability?
2. Representation of Magnetic Permeability
3. Unit of Magnetic Permeability
4. Explanation
5. How to measure permeability of any material ?
6. Permeability in Free Space or Vacuum
7. Relative Permeability
8. Factors affect on Permeability
9. Relation between Magnetic Permeability and Magnetic Susceptibility
10. Classification of material as per magnetic permeability

Representation of Magnetic Permeability :

Magnetic Permeability is represented by a Greek letter μ (italic). In 1885, Oliver Heaviside first coined this term as μ.

 As Magnetic flux is proportional to conductivity of the material ,

i.e.  magnetic flux ∝ conductivity of the material.

∴ Magnetic permeability ∝ No of lines passing through material.

Unit of Magnetic Permeability :

The SI units of magnetic permeability (μ) is Henry per meter (H/m) or Newton per ampere square(N/A²). 

Explanation :

A material having good magnetic permeability either gets magnetized in the opposite direction of the applied magnetic field or in the same direction of the applied magnetic field. In air or vacuum, magnetic permeability consider as poorest. Magnetic Permeability (μ) depends on many factors like strength of the applied magnetic field, the medium used, temperature and humidity. So Magnetic permeability is not constant. That's why in engineering application magnetic permeability is usually expressed in relative forms rather than in absolute form. Many magnetic alloys and purified iron have maximum relative magnetic permeability.

Based on magnetic permeability, magnetic materials are categorized as diamagnetic, paramagnetic, ferromagnetic and ferrimagnetics.

How to measure Permeability of any Material ?

In electromagnetism, Magnetization Force (H) means the ability of magnetic dipoles how they are organized in any material or medium due to magnetic flux density,B. 

Magnetic flux density, B is directly proportional to magnetization force H. 

Here μ = proportional constant of the material and it's termed as magnetic permeability.

So in other word we can say magnetic permeability (μ) is the ratio of magnetic flux density (B) of a magnetic material to it's magnetization force (H).

Permeability in Free space or Vacuum :

Permeability in free space(or in vacuum) is denoted as μ₀ that is also known as magnetic constant or permeability constant. The value of μ₀ is 4π 🗙 10⁻⁷ H/m ≈ 12.57 🗙 10⁻⁷ H/m .
(On 20 May 2019, a revision to SI unit went into effects its value, making the vacuum permeability no longer constant rather a value needs to be determine experimentally. In new system the new measured value is 4π 🗙 1.00000000082(20) 🗙 10⁻⁷ H/m. )

Relative Permeability :

Relative Permeability is denoted as μr.
Relative Permeability is the ratio of the permeability of any specific medium (μ) to the permeability of free space (μ₀).
                                                 ∴  μr = μ/μ₀
Hence the permeability of any medium/material , μ = μrμ₀
where  μ₀ = 4π 🗙 10⁻⁷ H/m.

Factors affecting on permeability :

Permeability of any medium or any material depends on several factors such as 

1. Temperature
2. Humidity
3. Nature of the material
4. position in the medium
5. Frequency of the applied field

Relation between Magnetic Permeability and Magnetic susceptibility :

χₘ = μr -1
Where χₘ = Magnetic susceptibility that is dimensionless quantity. 

Classification of Materials as per Magnetic Permeability :

Materials can be classified on the basis of their permeability such as 

Diamagnetic Material

This type of materials have constant relative permeability that is slightly less than 1 (μr < 1). So, in diamagnetic material magnetic flux density is slightly reduced.  Diamagnetic materials are repelled by external magnetic field .

Paramagnetic Material

This type of materials have constant relative permeability that is slightly greater than 1 but not exactly 1.  Paramagnetic materials are attracted by external magnetic field .

Ferromagnetic Material

This type of materials do not have constant relative permeability and μr is greater than 1(μr > 1).  Ferromagnetic materials are strongly attracted by external magnetic field .

Diamagnetic Material	Paramagnetic Material	Ferromagnetic Material
µr < 1	µr ≈ 1	µr > 1

Comparison of permeability between materials :

Where μf represents permeability of ferromagnetic material. 

          μₚ represents permeability of paramagnetic material,

          μ₀ represents permeability of free space,

    and μd represents permeability of diamagnetic material.

Know more about Types of Materials.