Magnetic Permeability is a fundamental concept in electromagnetism that describes how a material responds to the influence of an external magnetic field. The term was introduced by Oliver Heaviside in 1885, marking a significant contribution to the understanding of electromagnetic phenomena.

Magnetic permeability is essentially the ability of a material to allow the passage of magnetic lines of force. This property determines the material’s capacity to support and allow the passage of magnetic flux through it. In this article, we will discuss all the topics related to the concept of Magnetic Permeability.

What is Magnetic Permeability?

Magnetic permeability, in simple terms, is a measure of how easily a material can become magnetized when exposed to a magnetic field. It describes the material’s ability to allow or resist the flow of magnetic lines of force. Materials with high permeability can be easily magnetized, while those with low permeability resist magnetization.

Magnetic Permeability is crucial in understanding and designing magnetic devices, from everyday items like magnets to complex technologies such as transformers and inductors.

Magnetic Permeability Definition

Magnetic permeability is a property of a material that describes its ability to respond to a magnetic field by becoming magnetized.

It is represented by the symbol μ (mu) and is defined as the ratio of the magnetic flux density (B) to the magnetic field strength (H) in a given material.

The magnetic permeability of a material indicates how easily it can be magnetized. Materials with high permeability respond strongly to an applied magnetic field and can be easily magnetized, while materials with low permeability are less responsive to magnetic fields.

Magnetic Permeability of Free Space

The magnetic permeability of free space, denoted by the symbol μ₀ (mu naught), is a fundamental constant in physics. It has a value of approximately 4π x 10⁻⁷ T·m/A (tesla meter per ampere). This value serves as a reference point for comparing the magnetic permeabilities of other materials.

Magnetic Permeability Formula

Magnetic permeability is quantified using the formula:

μ = B/H

Where,

• μ is the magnetic permeability,
• B is the magnetic flux density,
• H is the magnetic field strength

Units of Magnetic Permeability

In the International System of Units (SI), Magnetic Permeability (μ) is measured in Henrys per meter (H/m). Other than that there are some more units as well such as:

• Gauss (G) or Maxwell per Square Centimeter (Mx/cm²) [Gaussian Unit]
• centimeter/gram [in CGS System]

Dimensions of Magnetic Permeability

The dimensions of magnetic permeability are [MLT⁻²A⁻²]

Types of Magnetic Permeability

There are two types of Magnetic Permeability that can be calculated for any material i.e.,

• Absolute Magnetic Permeability (μ)
• Relative Magnetic Permeability (μ_r)

Absolute Permeability (μ)

Absolute permeability (μ), often simply referred to as permeability, is a material-specific property that quantifies its intrinsic ability to carry magnetic flux.

The relationship between magnetic field strength (H), magnetic flux density (B), and absolute permeability (μ) is given by:

H = B / μ

Where:

• H is the magnetic field strength in amperes per meter (A/m).
• B is the magnetic flux density in teslas (T).
• μ is the absolute permeability in henrys per meter (H/m).

Relative Permeability (μᵣ)

Relative permeability is a dimensionless quantity that is defined as the ratio of material’s permeability to the permeability of a vacuum (μ₀).

Relative Permeability is often denoted as μᵣ and is given by:

μ_r = μ / μ₀

Where:

• μ is the absolute permeability of the material.
• μ₀ (mu-zero) is the absolute permeability of free space or vacuum, which is approximately 4π × 10^-7 H/m in SI units.

Note: Materials with μᵣ > 1 are considered magnetically susceptible, meaning they can amplify an applied magnetic field, while μᵣ < 1 indicates materials that weaken the field.

Magnetic Permeability Value

Magnetic permeability varies across different materials, influencing their response to magnetic fields, Absolute Magnetic Permeability of some of the common materials are listed as follows:

Relative Magnetic Permeability for Various  Materials

Relative magnetic permeability of some of the common materials are:

How to Measure Magnetic Permeability? 

Magnetic permeability is typically measured by examining how a material responds to an applied magnetic field. The two main parameters involved in the measurement are magnetic flux density (B) and magnetic field strength (H). Here’s a brief overview of how magnetic permeability is measured:

• Setup
  • Place the material sample in a controlled environment, free from external magnetic influences.
  • Apply a magnetic field (H) to the material using a magnetic source or coil.
• Magnetic Flux Density (B) Measurement
  • Measure the magnetic flux density (B) inside the material. This can be done using a device such as a gaussmeter or a Hall effect sensor.
• Magnetic Field Strength (H) Measurement
  • Measure the magnetic field strength (H) produced by the magnetic source or coil. This is typically done using an ammeter to measure the current in the coil or a magnetometer to measure the magnetic field.
• Calculate Magnetic Permeability (μ)
  • Use the formula: μ=B/H to calculate the magnetic permeability of the material.
  • Ensure that the units are consistent (e.g., in SI units, magnetic permeability is measured in henrys per meter, H/m).
• Repeat and Average
  • Perform multiple measurements to ensure accuracy and reliability.
  • Calculate the average magnetic permeability from the collected data.

This method will help us measure magnetic permeability in lab settings.

Magnetic Susceptibility

Magnetic susceptibility (χ) is a dimensionless quantity that indicates how much a material will become magnetized in response to an applied magnetic field.

Magnetic Susceptibility is a key parameter in understanding magnetic properties of materials, as it shows the degree of magnetization a material obtains in response to an applied magnetic field.

Relation between Magnetic Permeability and Susceptibility

The relationship between magnetic susceptibility (χ), absolute magnetic permeability (μ), and the permeability of free space (μ₀​) is given by the equation:

μ = μ₀​(1+χ)

Note: Magnetic Susceptibility can help us find the nature of material i.e.,

Magnetic Permeability: Conclusion

In conclusion, the concept of magnetic permeability is fundamental to understanding and manipulating magnetic fields in materials. This property, denoted as μ, quantifies the ability of a material to conduct magnetic lines of force, thereby influencing the magnetic response of the material to an external magnetic field.

Magnetic Permeability: FAQs

Why is it Called Permeability?

Magnetic permeability is named so because it measures how easily a material allows magnetic flux to permeate or flow through it.

What is the Formula for Magnetic Permeability?

The formula for magnetic permeability is μ=B/H, where B is the magnetic flux density, and H is the magnetic field strength.

What is Magnetic Permeability used for?

Magnetic permeability is used to describe how a material responds to an external magnetic field. It is a crucial parameter in the design and analysis of magnetic circuits, transformers, inductors, and other magnetic devices.

How is Magnetic Permeability Measured?

Magnetic permeability is often measured experimentally using a permeameter. The basic idea involves applying a known magnetic field to a material and measuring the resulting magnetic flux density. The ratio of the magnetic flux density to the applied magnetic field strength gives the magnetic permeability.

What are the Units of Magnetic Permeability?

The SI unit of magnetic permeability is henries per meter (H/m) or teslas per ampere (T/A). In some contexts, you might also encounter non-SI units like gauss per oersted (G/Oe).

Can materials have negative permeability?

Yes, certain materials, known as metamaterials, can exhibit negative permeability under specific conditions.