Magnetic Susceptibility: Definition, Formula, Types, Measurement and Applications

 

Introduction

Magnetic susceptibility is describes how a material responds when placed in an external magnetic field. Different materials exhibit different magnetic behaviours depending on their atomic structure and the arrangement of electrons. Some materials are strongly attracted by a magnetic field, some are weakly attracted, while others are repelled. Magnetic susceptibility provides a quantitative measure of this behaviour.

The study of magnetic susceptibility is essential in physics, electrical engineering, electronics, geology, chemistry, medicine, and material science. It helps in understanding magnetic materials used in transformers, motors, generators, magnetic storage devices, MRI scanners, and many other technological applications.

Definition of Magnetic Susceptibility

Magnetic susceptibility is defined as the ratio of the intensity of magnetization produced in a material to the applied magnetic field intensity.

Mathematically,                                χ_m = M/H
where

• χ_m = Magnetic susceptibility
• M = Magnetization of the material (A/m)
• H = Applied magnetic field intensity (A/m)

The above relation shows that susceptibility indicates how easily a material becomes magnetized when exposed to an external magnetic field.

 

Explanation of Magnetization

When a magnetic field is applied to a material, the magnetic dipoles inside the material tend to align themselves with the field.The magnetic moment per unit volume is called magnetization.
M = Magnetic Moment/Volume

A larger magnetization for a given magnetic field means a larger susceptibility.

Physical Meaning of Magnetic Susceptibility

Magnetic susceptibility provides information about:

•     The ease with which a material can be magnetized.
•       The strength of magnetic response.
•      Whether a material is attracted or repelled by a magnetic field.
•       The type of magnetic behavior exhibited by the material.

Interpretation:

• Positive susceptibility → Attraction toward magnetic field.
• Negative susceptibility → Repulsion from magnetic field.
• Large positive susceptibility → Strong magnetic behavior.
• Small susceptibility → Weak magnetic behavior.

 

Mathematical Relation with Magnetic Flux Density

The magnetic flux density is given by:   B = μ H
where

• B = Magnetic flux density
• μ = Permeability of material
• H = Magnetic field intensity

Also,
B = μ ₀(H + M)
Substituting
M = χ_m H
gives
B = μ ₀H+χ_m H)

B= μ ₀ (1+ χ_m )H
Therefore

μ  = μ ₀ (1+ χ_m)

This equation establishes the relationship between magnetic susceptibility and permeability.

Relative Permeability and Susceptibility

Relative permeability is defined as

μ _r= μ / μ ₀
Using
μ = μ ₀ (1+ χ_m)
we obtain

μ _r=1+ χ_m
or

χ_m = μ _r -1
This relation is very useful in magnetic material calculations.

Units of Magnetic Susceptibility

From

χ_m =M/H
Both (M) and (H) have the same units (A/m).

Therefore,

χ_m has no unit.

Hence magnetic susceptibility is a dimensionless quantity.

Types of Magnetic Materials Based on Susceptibility

Materials can be classified according to their susceptibility values into:

1. Diamagnetic materials
2. Paramagnetic materials
3. Ferromagnetic materials
4. Antiferromagnetic materials
5. Ferrimagnetic materials

Diamagnetic Materials

Diamagnetic materials possess negative magnetic susceptibility.

For these materials,

χ_m < 0

Characteristics:

• Weakly repelled by magnetic field.
• No permanent magnetic dipole moment.
• Magnetization opposite to applied field.
• Susceptibility is very small and negative.

Examples:

• Bismuth
• Copper
• Silver
• Gold
• Water
• Mercury

Typical values:

χ_m  ≈ -10^-5

Origin of Diamagnetism

In diamagnetic substances, electrons move in orbital paths around the nucleus.

When an external magnetic field is applied, induced currents are produced.

According to Lenz's law, these currents create a magnetic field opposite to the applied field.

Therefore diamagnetic materials are repelled by magnetic fields.

 

Paramagnetic Materials

Paramagnetic materials have small positive susceptibility.

χ_m > 0

Characteristics:

• Weakly attracted by magnetic field.
• Possess permanent magnetic dipoles.
• Magnetization occurs in direction of applied field.
• Susceptibility is positive but small.

Examples:

• Aluminum
• Platinum
• Magnesium
• Chromium
• Oxygen

Typical values:  χ_m  ≈ -10^-5to 10^-3

Origin of Paramagnetism

Atoms contain unpaired electrons.

Each unpaired electron acts like a tiny magnet.

Without an external field, these magnetic moments are randomly oriented.

When a magnetic field is applied, the moments partially align with the field.

This produces a net positive magnetization.

Curie's Law

For paramagnetic materials, susceptibility varies inversely with temperature.

Curie's Law states

χ_m  =C/T

where

• C= Curie constant
• T = Absolute temperature

According to this law:

• Higher temperature → Lower susceptibility.
• Lower temperature → Higher susceptibility.

The thermal motion disturbs alignment of magnetic moments.

Ferromagnetic Materials

Ferromagnetic materials possess extremely large positive susceptibility.

χ_m​≫1

Characteristics:

• Strong attraction toward magnetic field.
• Very high magnetization.
• Permanent magnetic domains.
• Retain magnetization even after field removal.

Examples:

• Iron
• Nickel
• Cobalt
• Steel

Typical susceptibility: 10³ to 10⁶

Domain Theory of Ferromagnetism

Ferromagnetic materials consist of microscopic regions called domains.

Inside each domain:

• Magnetic moments are aligned.
• Strong magnetization exists.

Without an external field:

• Domains are randomly oriented.
• Net magnetization is nearly zero.

When a magnetic field is applied:

• Domains align with the field.
• Magnetization increases rapidly.

This results in very high susceptibility.

Curie Temperature

Ferromagnetic materials lose their ferromagnetic properties above a certain temperature.

This temperature is called Curie temperature.

Examples:

• Iron: 770°C
• Nickel: 358°C
• Cobalt: 1120°C

Above Curie temperature:

• Ferromagnetic behavior disappears.
• Material becomes paramagnetic.

Antiferromagnetic Materials

In antiferromagnetic materials:

• Neighboring magnetic moments align in opposite directions.
• Equal magnetic moments cancel each other.

Characteristics:

• Very small susceptibility.
• Net magnetization nearly zero.

Examples:

• Manganese oxide (MnO)
• Nickel oxide (NiO)
• Chromium

Ferrimagnetic Materials

Ferrimagnetic materials also have opposite magnetic moment alignment.

However:

• Opposing moments are unequal.
• Complete cancellation does not occur.

Examples:

• Magnetite
• Ferrites

These materials exhibit moderate susceptibility.

Volume Magnetic Susceptibility

Volume susceptibility is defined as

 χ_v​=HM​

It represents magnetization per unit volume.

This is the most commonly used susceptibility.

Mass Magnetic Susceptibility

Mass susceptibility is susceptibility per unit mass. χ_mass​=χ_v​​ /ρ

where

• ρ is density.

Unit:m³/kg
Molar Magnetic Susceptibility

Molar susceptibility is defined as χ_molar​=M_w​χ_mass​

where

• M_w​ is molecular weight.

Unit: m₃/mol
This quantity is extensively used in chemistry.

Measurement of Magnetic Susceptibility

Several methods are used to measure magnetic susceptibility.

Gouy Method

In this method:

• Sample is suspended in a magnetic field.
• Magnetic force acting on sample is measured.

Suitable for solids and powders.

Faraday Method

Uses force experienced by material in a non-uniform magnetic field.

Susceptibility is calculated from force measurements.

Quincke's Method

Used for liquids.

The rise of liquid in a magnetic field is measured.

The susceptibility is calculated from height difference.

Vibrating Sample Magnetometer (VSM)

Modern technique.

Measures magnetic moment by vibrating sample inside magnetic field.

Provides highly accurate results.

Applications of Magnetic Susceptibility

1. Material Identification

Susceptibility helps classify materials as:

• Diamagnetic
• Paramagnetic
• Ferromagnetic

2. Geological Exploration

Magnetic susceptibility measurements help locate:

• Iron ore deposits
• Mineral resources
• Underground structures

3. Medical Imaging

MRI technology relies on magnetic properties of tissues.

Differences in susceptibility improve image contrast.

4. Magnetic Storage Devices

Hard disks and magnetic memories use materials with suitable susceptibility.

5. Transformer Cores

High susceptibility materials provide better magnetic flux concentration.

6. Electrical Machines

Motors and generators require magnetic materials with high susceptibility.

7. Magnetic Sensors

Magnetic susceptibility is important in sensor design and calibration.

8. Superconductivity Research

Susceptibility measurements help identify superconducting transitions.

Advantages of High Magnetic Susceptibility

• Easy magnetization.
• Strong magnetic response.
• Efficient magnetic flux guidance.
• Improved machine performance.
• Reduced magnetic losses.

Limitations

• Susceptibility may vary with temperature.
• Depends on magnetic field strength.
• Ferromagnetic materials exhibit non-linear behavior.
• Hysteresis affects measurements.

Comparison of Different Magnetic Materials

Material Type	Susceptibility
Diamagnetic	Negative and very small
Paramagnetic	Positive and small
Ferromagnetic	Very large positive
Antiferromagnetic	Small positive
Ferrimagnetic	Moderate positive

 

Importance in Electromagnetic Theory

Magnetic susceptibility links microscopic magnetic properties with macroscopic magnetic behavior.

It helps in:

• Understanding magnetic materials.
• Designing electromagnetic devices.
• Developing advanced magnetic technologies.
• Studying atomic and electronic structures.

Conclusion

Magnetic susceptibility is a fundamental property that describes the response of a material to an applied magnetic field. It is defined as the ratio of magnetization to magnetic field intensity and provides valuable information about the magnetic nature of materials. Depending on the sign and magnitude of susceptibility, materials are classified as diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, or ferrimagnetic. The concept plays a vital role in electromagnetics, material science, electrical engineering, geology, medicine, and modern technology. Understanding magnetic susceptibility enables scientists and engineers to select suitable magnetic materials for applications ranging from transformers and motors to MRI systems and magnetic storage devices.