Derive the relation between magnetic field intensity (H) and magnetization (M) for a magnetic material placed in a magnetizing field.

To derive the relationship between magnetic field intensity (H) and magnetization (M) for a magnetic material in a magnetizing field, we need to delve into some fundamental concepts of magnetism. This relationship is crucial for understanding how materials respond to external magnetic fields and how they become magnetized.

Understanding Magnetic Field Intensity and Magnetization

Magnetic field intensity (H) is a measure of the strength of the magnetic field produced by an external source, while magnetization (M) represents the degree to which a material becomes magnetized in response to that field. The relationship between these two quantities can be expressed through the concept of magnetic susceptibility (χ), which quantifies how easily a material can be magnetized.

The Basic Equation

The relationship can be expressed mathematically as:

• M = χH

Here, M is the magnetization of the material, χ is the magnetic susceptibility, and H is the magnetic field intensity. This equation indicates that the magnetization of a material is directly proportional to the magnetic field intensity applied to it, scaled by the susceptibility of the material.

Incorporating the Magnetic Field (B)

To further understand this relationship, we can also consider the magnetic flux density (B), which is related to both H and M. The relationship is given by:

• B = μ₀H + M

In this equation, μ₀ is the permeability of free space. By substituting M from the first equation into this equation, we can express B in terms of H:

• B = μ₀H + χH
• B = (μ₀ + χ)H

Defining Permeability

The term (μ₀ + χ) can be defined as the permeability (μ) of the material:

• μ = μ₀(1 + χ)

Thus, we can rewrite the relationship between H, M, and B as:

• B = μH

Implications of the Relationship

This relationship shows that the magnetization of a material is not only dependent on the external magnetic field but also on the intrinsic properties of the material itself, represented by its susceptibility. Different materials will respond differently to the same magnetic field intensity due to their unique magnetic properties.

Example: Ferromagnetic Materials

For instance, ferromagnetic materials, such as iron, have a high susceptibility, meaning they can become highly magnetized even with a relatively small external magnetic field. In contrast, diamagnetic materials exhibit a negative susceptibility and will have a very weak magnetization in the presence of an external field.

Summary of Key Points

• The relationship between magnetic field intensity (H) and magnetization (M) is given by M = χH.
• Magnetic flux density (B) relates to H and M through B = μ₀H + M.
• Permeability (μ) of a material is defined as μ = μ₀(1 + χ).
• Different materials respond differently to magnetic fields based on their susceptibility.

This understanding of the relationship between H and M is fundamental in fields such as material science, electrical engineering, and physics, where magnetic properties play a crucial role in the design and application of various technologies.