## What is Magnetic Permeability?

Also known as electromagnetism, magnetic permeability is the measure of a material’s resistance against the formation of a magnetic field. It can be defined as a relative increase or decrease in the resultant magnetic field (M.F.) inside any material as compared to the magnetizing field in which the given material is located. The magnetic permeability definition can be written as the property of a material that is equal to the magnetic flux density B established within the material by a magnetizing field split into the magnetic field strength H of the magnetizing field.

The ratio of magnetic induction to magnetic intensity is known as Magnetic Permeability. A measure of a particular material's resistance against the formation of a magnetic field. In the year 1885, Magnetic Permeability was coined by Oliver Heaviside. Magnetic permeability is a property that basically allows magnetic lines of force to pass through a material. Magnetic Permeability is also known as Electromagnetism.

The property of a material that is equal to the magnetic flux density B established within the material by a magnetizing field that is split into the magnetic field strength H of the magnetizing field, is known as Magnetic Permeability.

The Magnetic permeability formula is as follows :

Magnetic permeability (μ), which is pronounced as mu = B/H

Where B = magnetic intensity and H = magnetizing field.

Henries per meter (H/m) or newtons per ampere squared (N⋅A−2) is the SI unit of magnetic permeability.

Permeability can be of different types:

### Permeability of Free Space

Also known as the permeability of air or of vacuum, the permeability of free space is represented by μ0=B0/H - the ratio of magnetic intensity in a vacuum and magnetizing field.

### Permeability of Medium

It is expressed as;

μ = B/H - the ratio of the magnetic intensity in the medium and magnetizing field.

### Relative Permeability

This is expressed as;

μr= μ/μm, where the Relative permeability is known to be a dimensionless quantity and it is the ratio of two quantities with the same units, and hence, the relative permeability has no unit.

1 is the Relative permeability of free space.

### Classification of Magnetic Materials

Magnetic materials, based on their magnetic permeabilities, can be classified in the following ways:

i) Diamagnetic Material: Diamagnetic Material has a constant relative magnetic permeability that is slightly lesser than 1. For example, Bismuth. When Bismuth is placed in any magnetic field, external M.F. is partially expelled and the magnetic flux density that is inside is reduced. Diamagnetism is said to cause a repulsive effect as it creates a magnetic field in opposition to an externally applied magnetic field.

ii) Paramagnetic Material: The constant relative permeability of Paramagnetic Material is slightly more than 1. For example, Platinum. When the Platinum is placed in a magnetic field, it becomes magnetized in the direction of the external M.F.

iii) Ferromagnetic Material: The Ferromagnetic Material does not have any kind of constant relative permeability. For example, Iron. In iron, As the magnetizing field increases, we see that the relative permeability also increases and this reaches a maximum point and decreases later on. Lots of magnetic alloys, including that of purified iron, all have a maximum relative permeability of over 100,000.

### Magnetic Permeability Formula

Magnetic permeability is represented as μ (it is pronounced as mu) and can be expressed as μ = B/H, where, B is the magnetic flux density which is a measure of the actual magnetic field within a material and is considered as a concentration of magnetic field lines or magnetic flux per unit cross-sectional area. H is the magnetic field strength which is a measure of the magnetizing field produced by electric current flow in a wire or coil.

### S.I. Unit of Magnetic Permeability

The SI unit of magnetic permeability is known to be Henries per meter (H/m) which can also be represented as newtons per ampere square.

### Classification of Magnetic Materials

Based on the magnetic permeabilities, materials can be classified as follows.

Diamagnetic Material: It has a constant relative magnetic permeability slightly lesser than 1. An example of a diamagnetic material is bismuth and when it is placed in a magnetic field, the external M.F. is partly expelled and the magnetic flux density within it reduces. Diamagnetism, thus, causes a repulsive effect by creating a magnetic field in opposition to an externally applied magnetic field.

Paramagnetic Material: It has a constant relative permeability which is slightly more than 1. An example of paramagnetic material is Platinum and when it is placed in a magnetic field, it becomes magnetized in the direction of the external M.F.

Ferromagnetic Material: It doesn’t have a constant relative permeability. An example of ferromagnetic material is iron. As the magnetizing field increases, the relative permeability increases and reaches a maximum and later decreases. Many magnetic alloys including purified iron have a maximum relative permeability of over 100,000.

### Factors that Affect Magnetic Permeability

The factors affecting the magnetic permeability are as follows.

Nature of the material

Humidity

Position in the material

Temperature

Frequency of the applied force

Magnetic Field (Magnetic permeability is normally positive that can vary with an M.F. The opposite of magnetic permeability is magnetic reluctivity.)

### What is Complex Permeability?

Complex permeability is a useful tool that deals with high-frequency magnetic effects. At low frequencies in a linear material, it is found that the auxiliary magnetic field and the magnetic field are proportional to each other through some scalar permeability, and at high frequencies, these quantities are known to react to each other with some lag time.

### Different Types of Permeability

Free Space Permeability: It is the permeability of free space, vacuum, or air and is represented by μ₀=B₀/H. It refers to the magnetic intensity in a vacuum and magnetizing field.

Medium Permeability: It is the ratio of magnetic intensity in the medium and magnetizing field. Permeability of the medium is represented as μ = B/H.

Relative Permeability: It is a dimensionless quantity, and is defined as the ratio of two quantities with the same units. This leads to no unit existence of relative permeability. The relative permeability of free space is known to be 1.

It is expressed as μᵣ = μ/μₘ.

(The number of lines of magnetic induction per unit area in a material divided by the number of lines per unit area in a vacuum.)

## FAQs on Magnetic Permeability

**1. What is Magnetic Susceptibility?**

It is a quantity that measures how much a material will be magnetized in an applied magnetic field. It is the ratio of magnetization M to the applied magnetizing field intensity, denoted by H. Magnetization is the magnetic moment per unit volume. The interactions of electrons and nuclei when an external magnetic field is applied, causes magnetic susceptibility. It is represented as, χₘ = M/H.

**2. What is the Relation Between Relative Permeability and Magnetic Susceptibility?**

The relationship between magnetic susceptibility and relative permeability can be represented as χₘ = μᵣ − 1. The ratio of effective permeability of a particular fluid at a particular saturation to that of absolute permeability of the fluid at total saturation is the relative permeability and it is such that if a single fluid is found in a rock, it’s relative permeability is 1.0. Relative permeability is represented as µ₀. µᵣ = µ / µ₀ (1) where µr is the relative permeability and µ is the permeability of the medium (H/m).

**3. What are the factors that affect Relative Permeability?**

Permeability is said to be dependent on various factors. Some of the major factors that affect Magnetic Permeability are the following :

The nature of the material

The humidity of the material

The position that is in the medium

Temperature is another factor

The Frequency of the applied force, and

The Magnetic Field (Normally positive, the Magnetic permeability can vary with an M.F.

**4. What do you mean by Complex Permeability?**

A useful tool that deals with high-frequency magnetic effects is what we understand as Complex Permeability. It is found that the auxiliary magnetic field and the magnetic field are proportional to each other through some scalar permeability when it is at low frequencies in a linear material, and when it is at higher frequencies, then these quantities are known to react with each other with some lag time.

Complex Permeability can be represented as one very complex parameter that consists of one real and one imaginary part.

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**6. Explain the Magnetic Permeability of a material?**

The magnetic permeability can be described as the measure of the resistance of a particular material against the formation of a magnetic field. A relative increase or decrease in the resultant magnetic field (M.F.) which can be found inside any material as compared to the magnetizing field in which the given material is located, explains what Magnetic Permeability is.

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