# Magnetic Permeability

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## 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.

### 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.

1. 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.

2. 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.

3. 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

1. 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.

2. 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.

3. 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/μ.

(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.)