Understanding Magnetisation: Intensity vs. Force

The question asks us to identify a specific dimensionless constant that describes how easily a material can be magnetised when an external magnetic field is applied. This constant is defined as the ratio of the intensity of magnetisation ($M$) developed within the material to the applied magnetising force ($H$).

Key Concepts: Magnetisation ($M$) and Magnetising Force ($H$)

• Magnetising Force ($H$): This represents the strength of the external magnetic field applied to a material. It is often thought of as the 'cause' of magnetisation. Its SI unit is Amperes per meter (A/m).
• Intensity of Magnetisation ($M$): This represents the degree to which a material becomes magnetised when subjected to a magnetising force. It essentially measures the magnetic dipole moment per unit volume within the material. It is the 'effect' produced in the material. Its SI unit is also Amperes per meter (A/m).

Defining the Constant: Magnetic Susceptibility

The question defines a specific constant as the ratio of the intensity of magnetisation ($M$) to the applied magnetising force ($H$). Mathematically, this is expressed as:

Let's analyze this ratio:

• Units: Since both $M$ and $H$ have the same units (A/m), their ratio, $\chi_m$, is dimensionless. This matches the description given in the question.
• Meaning: A higher value of $\chi_m$ indicates that a material magnetises more strongly for a given applied field ($H$). This means the material is easily magnetised. Conversely, a low $\chi_m$ means the material requires a strong field to achieve significant magnetisation.

This quantity, Magnetic Susceptibility, precisely fits the definition and description provided.

Evaluating Other Options

Let's look at why the other options are not the correct answer:

Magnetic Permeability ($\mu$)

Magnetic permeability ($\mu$) is defined as the ratio of magnetic flux density ($B$) to the magnetising force ($H$):

This constant describes how easily a magnetic field can be established in a material. However, it is not dimensionless. Its SI unit is Henries per meter (H/m). It also involves magnetic flux density ($B$), not directly the intensity of magnetisation ($M$) in the way the question describes.

Relative Permeability ($\mu_r$)

Relative permeability ($\mu_r$) is the ratio of the absolute permeability of the material ($\mu$) to the permeability of free space ($\mu_0$):

This is a dimensionless quantity. It compares the permeability of a material to that of vacuum. While related to magnetic susceptibility through the equation $\mu_r = 1 + \chi_m$, it is not defined directly as the ratio $\frac{M}{H}$.

Magnetic Flux Density ($B$)

Magnetic flux density ($B$) represents the total magnetic field within a material. It is related to both the magnetising force ($H$) and the intensity of magnetisation ($M$) by the equation:

where $\mu_0$ is the permeability of free space. Magnetic flux density is not a dimensionless constant; its SI unit is the Tesla (T).

Comparison Summary

Based on the definition provided in the question – the ratio of the intensity of magnetisation ($M$) to the applied magnetising force ($H$) being a dimensionless constant – the correct term is Magnetic Susceptibility.