Relative Permeability Explained

The relative permeability, denoted by $\mu_r$, is a crucial property that helps us understand how a material responds to an external magnetic field. It is defined as the ratio of the magnetic permeability of a material ($\mu$) to the permeability of free space ($\mu_0$). Mathematically, it is expressed as:

$ \mu_r = \frac{\mu}{\mu_0} $

Here, $\mu_0$ is a constant value equal to $4\pi \times 10^{-7}$ T·m/A. The relative permeability tells us how much a material can concentrate magnetic flux lines or, in simpler terms, how easily a material can be magnetized. Based on their relative permeability, materials are broadly classified into three main categories: paramagnetic, diamagnetic, and ferromagnetic.

Paramagnetic Materials Characteristics

Paramagnetic materials are those that are weakly attracted to an external magnetic field. A key characteristic of paramagnetic materials is that their relative permeability ($\mu_r$) is slightly greater than unity (i.e., $\mu_r > 1$). This means that the magnetic field inside a paramagnetic material is slightly stronger than the external magnetic field applied.

• These materials have permanent magnetic dipoles (due to unpaired electrons) that are randomly oriented in the absence of an external field.
• When an external magnetic field is applied, these dipoles align themselves partially in the direction of the field, leading to a weak magnetization.
• The magnetization disappears once the external field is removed.
• Common examples include Aluminum, Oxygen, Platinum, and Sodium.

Diamagnetic Materials Characteristics

Diamagnetic materials are distinct because they are weakly repelled by an external magnetic field. For diamagnetic materials, the relative permeability ($\mu_r$) is slightly less than unity (i.e., $\mu_r < 1$). This indicates that the magnetic field inside a diamagnetic material is slightly weaker than the external magnetic field.

• These materials do not have permanent magnetic dipoles.
• When an external magnetic field is applied, it induces a weak magnetic moment in the opposite direction of the applied field, causing repulsion.
• This induced magnetic moment also disappears when the external field is removed.
• Common examples include Bismuth, Copper, Water, Gold, and most organic compounds.

Ferromagnetic Materials Characteristics

Ferromagnetic materials are strongly attracted to magnetic fields and can retain their magnetism even after the external field is removed, forming permanent magnets. Their relative permeability ($\mu_r$) is much greater than unity (i.e., $\mu_r \gg 1$), often ranging from hundreds to thousands.

• These materials have strong permanent magnetic dipoles that are aligned in microscopic regions called domains.
• When an external field is applied, these domains grow and align with the field, leading to strong magnetization.
• Examples include Iron, Nickel, Cobalt, and their alloys.

Comparing Magnetic Material Properties

To summarize the properties of different magnetic materials based on their relative permeability:

Classifying Materials A and B

The question provides specific information about the relative permeability of two materials, A and B:

• For Material A: Its relative permeability is slightly more than unity.
  This condition, $\mu_r > 1$ (slightly), directly matches the definition of a paramagnetic material.
• For Material B: Its relative permeability is slightly less than unity.
  This condition, $\mu_r < 1$ (slightly), directly matches the definition of a diamagnetic material.

Conclusion on Material Types

Based on the analysis of relative permeability values:

• Material A, with $\mu_r$ slightly more than unity, is classified as a paramagnetic material.
• Material B, with $\mu_r$ slightly less than unity, is classified as a diamagnetic material.

Therefore, the statement "Material A is paramagnetic and B diamagnetic" accurately describes the nature of these materials.