Magnetic Permeability

Magnetic permeability is an important property in the study of magnetism. Oliver Heaviside invented the term in the year 1885. It tells us how easily a material can allow magnetic field lines to pass through it. In simple terms, it measures the ability of a material to become magnetised or to conduct magnetic lines of force. The magnetic permeability of a material can also be called its magnetisation capability.

Definition

Magnetic permeability is used to calculate the ease of magnetisation. It is defined as the ratio of the magnetic induction (B) to the magnetic intensity (H). It is a scalar quantity and is denoted by μ.

Formula

formula

where:

μ - Magnetic permeability of the material (H/m)
B - Magnetic flux density (T)
H - Magnetic field strength (A/m)

If the material has high magnetic permeability, then higher will be the conductivity for magnetic lines of force.

Factors Affecting Magnetic Permeability

Magnetic field strength – μ increases initially, then decreases after saturation.
Temperature – μ drops sharply above the Curie temperature.
Material composition – Different materials have different μ values.
Frequency – High frequency reduces μ due to eddy current losses.

Types of Magnetic Permeability

The key types are as follows:

Permeability of Medium

The ratio of magnetic intensity (B) in the medium and magnetising field (H) is known as the permeability of the medium.

formula

Permeability of Free Space

The permeability of free space is also known as the permeability of air or vacuum. It is the ratio of magnetic intensity (B₀) in a vacuum and magnetising field (H).

formula

μ₀ = 4π × 10⁻⁷ H/m

Relative Permeability

It is the ratio of two quantities with the same units. Relative permeability is dimensionless. The relative permeability of free space is 1.

formula

μ_r > 1: Material is paramagnetic or ferromagnetic (supports magnetism).
μ_r < 1: Material is diamagnetic (opposes magnetism).

Permeability in Different Materials

Materials are classified according to their permeability:

Diamagnetic Material

Diamagnetic materials have a constant relative permeability (μ_r) of slightly less than vacuum, 1 (μ_r slightly < 1), and that’s why the magnetic flux density inside diamagnetic materials is slightly reduced. Diamagnetic materials are weakly repelled in external magnetic fields due to induced magnetic moments in the opposite direction. Examples - Copper, Bismuth, Silver

Paramagnetic Material

Paramagnetic materials have a constant relative permeability (μ_r) slightly greater than vacuum 1 (μ_r slightly > 1). For the same reason, if a paramagnetic material is kept in an external field, it gets weakly attracted to magnetic fields due to unpaired electrons aligning slightly with the field. The Weak Effect disappears when the external field is removed. Examples - Aluminium, Platinum, Tungsten

Ferromagnetic Material

Ferromagnetic materials have no constant relative permeability (μ_r). They have very high permeability (μ_r can be in thousands or more). When the magnetising field increases, the relative permeability also increases. Therefore, the strongest magnetic properties are in ferromagnetic materials. It can be permanently magnetised. Examples - Soft iron (μ_r ≈ 200,000 depending on purity) is used in transformer cores, Iron, Cobalt, and Nickel

Relationship Between B, H, and μ

B = μ H

If μ is constant, B increases linearly with H.
In ferromagnetic materials, μ can change with H, leading to non-linear behaviour (hysteresis).

Applications

Electromagnet Design: Choosing core materials with high permeability increases magnetic field strength.
Transformer Efficiency: High-permeability cores reduce energy loss.
Magnetic Shielding: High-permeability materials can block or redirect magnetic fields.
Communication Devices: Permeability affects inductors, antennas, and transmission lines.