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# What is Permeability and Magnetic Susceptibility?

Magnetic permeability is sometimes also referred to as permeability in electromagnetism, which is defined as a property of a magnetic material which supports the formation of a magnetic field. Magnetic permeability is a property that basically allows magnetic lines of force to pass through a 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 can pass through the material. In this article, you will learn what is permeability, its units, magnetic susceptibility and classification of magnetic materials.

### What is permeability?

Magnetic permeability is the ability of a magnetic substance to facilitate the creation of a magnetic field. The conductivity for magnetic lines of force increases as the magnetic permeability of the material increases and vice versa. The ease with which an external magnetic field can induce a stronger magnetic force of attraction in a material is measured by its magnetic permeability. Magnetic permeability is measured in Henry per meter in SI units. The symbol for it is μ.

μ can be defined in a variety of ways. “Magnetic permeability is defined as the ratio of magnetic induction to magnetic field intensity,” according to one of the Magnetic Permeability Definitions.  It is a scalar quantity. Another Magnetic Permeability Definition states that it is a property that allows us to determine a material’s resistance to an external magnetic field or the degree to which a magnetic field can pass through it. The conductivity for magnetic lines of force will be stronger if the material has a higher μ.

### Factors Affecting Permeability

The nature of the material, humidity, position in the medium, temperature, and frequency of the applied force are all factors that influence permeability. μ is always positive and varies with the presence of a magnetic field. Magnetic reluctivity, on the other hand, is the polar opposite of μ.

Magnetic permeability is defined as a relative rise or fall in the resultant magnetic field inside the materials compared to the magnetizing field, in which material is placed. It is the degree of magnetization in response to the applied field. Magnetic permeability formula is given as

μ = B / H

Here, B is the magnetic flux density that is built inside material and H is the strength of magnetizing field.

H is the measure of that magnetizing field which is produced due to the electric current flow.

B is the measure of that magnetic field which is taken under concentration of magnetic field lines per unit cross sectional area.

Φ = B . A

B = Φ / A

In free space, both magnetizing field and magnetic flux density i.e. B and H are same because there is no matter to modify the field.

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### Unit of magnetic permeability

In CGS unit system, μ is a dimensionless quantity. However in MKS system, B and H have different units so permeability was defined as 4 π ×10-7 weber per ampere meter. The permeability is also measured in terms of Henry / meter or newton per ampere squared, which has dimensions of inductance per unit length.

### What is relative permeability?

The ratio of magnetic flux density to magnetic field strength (B/H) is referred to as absolute permittivity. Relative permeability μr is a ratio given as μ/ μo , so it is dimensionless quantity whose value is 1 for space. Here μ0 indicates the permeability of free space and μ indicates the permeability of medium.

μr = μ / μo

### What is magnetic susceptibility?

Magnetic susceptibility specifies whether a material will be attracted into or repelled out of a magnetic field. It is the measure of how much a material will become magnetized by the application of applied magnetic field. Mathematically, it is the ratio of M to H.

“M” is magnetic moment per unit volume.

“H” is intensity of magnetizing field.

It is indicated by χ and is magnetic susceptibility formula is given as

χ = M / H

The above equation relates magnetic susceptibility and permeability.

### Classification of materials

On the basis of χ and magnetic behaviors, materials can be classified into following categories.

Diamagnetic materials: Such materials have μr less than 1. When such materials are placed in external magnetic field, external field is partly expelled due to which flux density is slightly reduced in the material. Material creates a magnetic field in opposite direction to the applied field. χ is negative for diamagnetic materials. In this case, the magnetic field in the material is weakened by the external magnetization. Example of such materials include bismuth.

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Paramagnetic materials: The value of μr for Such materials is more than one. Such material becomes slightly magnetized in direction of applied field, when it is placed in external magnetic field. Magnetic susceptibility of paramagnetic material is positive, which means the magnetic field in the material is strengthened by the induced magnetization. E.g. platinum.

Ferromagnetic materials: These materials don’t have constant μr. μr increases as external magnetizing field increases, then decreases after reaching a maximum value. Magnetic susceptibility is very high and positive and depends on the external field. E.g. iron and cobalt.