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Magnetic Susceptibility Explained for Class 12, JEE & NEET

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Magnetic Susceptibility Formula, Unit, and Classification of Materials

Magnetic susceptibility describes how much a material becomes magnetized when exposed to an external magnetic field. This property is fundamental in classifying and understanding the magnetic behavior of substances, and it plays a key role in physics, engineering, geology, and environmental sciences. The concept helps explain why some materials are attracted to magnets, while others are repelled, and why certain materials are useful in devices like transformers, MRI machines, and environmental sensors.


Magnetic Susceptibility: Definition and Formula

Magnetic susceptibility (symbol: χ) is a dimensionless quantity that measures the ratio of the magnetization (M) induced in a material to the applied magnetic field strength (H). This relationship is given by:

χ = M / H

Where:

M = Magnetization (magnetic moment per unit volume)
H = Applied magnetic field strength
If χ is positive, the material is magnetized in the same direction as the field (attracted). If χ is negative, it becomes magnetized in the opposite direction (repelled).


Magnetic Permeability and Its Relation to Susceptibility

Another important concept is magnetic permeability (μ), which links magnetic field intensity (H) to magnetic flux density (B) within a material:

B = μH

Relative permeability (μr) is the ratio of a material’s permeability to that of vacuum (μ0), and relates directly to susceptibility:

χ = μr - 1

Understanding these properties is crucial for analyzing how different materials respond to magnetic fields, which is essential in designing electrical and magnetic devices.


Types of Magnetic Susceptibility

Materials display different magnetic behaviors based on their electronic structure and magnetic susceptibility:

Type Susceptibility (χ) Description Examples
Diamagnetic χ < 0 (negative) Weak, opposed to field Copper, Bismuth, Water
Paramagnetic χ > 0 (small, positive) Weakly aligned with field Aluminium, Oxygen
Ferromagnetic χ ≫ 1 (large, positive) Strongly aligned, permanent magnets Iron, Nickel, Cobalt
Antiferromagnetic Special case Adjacent ions aligned oppositely Manganese oxide
Ferrimagnetic Intermediate Opposite but unequal alignment Ferrites (e.g., magnetite)

Applications of Magnetic Susceptibility

  • Identifying mineral deposits by measuring the content of magnetic minerals like iron and nickel.
  • Assessing environmental pollution by detecting magnetic particles in water, soil, and sediments.
  • Studying climate history through sediment cores, since changes in magnetic properties reflect shifts in climate conditions.
  • Medical and biological research, particularly in the development of superparamagnetic nanoparticles for targeted therapies.
  • Archaeology, for locating and mapping buried structures or artifacts containing magnetic materials.

Magnetic susceptibility is also valuable in the design of magnetic storage, motors, sensors, and for non-invasive analysis of various materials.


How to Measure Magnetic Susceptibility

Magnetic susceptibility can be measured using specialized instruments (e.g., susceptibility meters, magnetometers) on both solid and liquid samples. Data can be used alone or combined with chemical and structural analyses for more detailed material identification.

In practice, measurements help track sources of sediment, monitor industrial pollution, and assess suitability of materials for electronic applications.


Step-by-Step Approach to Problems

  1. Identify magnetization (M) and applied magnetic field (H) in the problem.
  2. Apply the formula χ = M / H for direct calculation.
  3. If dealing with permeability, use μ = μ0 × μr and χ = μr – 1 to relate quantities as needed.
  4. For more complex cases (e.g., paramagnetic substances), use temperature-dependent formulas if provided.

If more data is required (e.g., Curie's law), ensure units are consistent before solving.


Key Formulas in Magnetic Susceptibility

Formula Meaning/Application
χ = M / H Basic definition (magnetization per applied field)
B = μH Relating magnetic flux (B) to field strength (H)
χ = μr - 1 Relation between susceptibility and relative permeability

Example Problem

A sample has M = 20 A/m and is placed in an external magnetic field H = 1000 A/m. What is its magnetic susceptibility?

χ = M / H = 20 / 1000 = 0.02 (dimensionless)

This indicates the material has a small, positive susceptibility and is classified as paramagnetic.


Using Magnetic Susceptibility with Other Methods

Magnetic susceptibility is often combined with chemical, structural, and microscopic analyses. For example, mineral exploration pairs susceptibility data with geological and geochemical information to accurately locate ores. In environmental studies, combining magnetic and chemical techniques improves detection of pollutants and understanding of past environmental changes.


Further Learning and Practice


Learning magnetic susceptibility gives insight into material behaviors under magnetic fields, supports hands-on problem-solving, and forms a foundation for advanced applications in science, engineering, and medicine.

FAQs on Magnetic Susceptibility Explained for Class 12, JEE & NEET

1. What is magnetic susceptibility in physics?

Magnetic susceptibility is a dimensionless quantity that indicates how much a material will become magnetized when placed in an external magnetic field. It is defined as the ratio of magnetization (M) to the applied magnetic field intensity (H): χ = M / H.

2. What is the SI unit of magnetic susceptibility?

Magnetic susceptibility is a dimensionless quantity and has no SI unit. It expresses a relative property rather than an absolute measurement.

3. How is magnetic susceptibility measured?

Magnetic susceptibility is commonly measured using instruments like a Gouy balance or a magnetic susceptibility meter by:

  • Placing the material sample in a known magnetic field
  • Measuring the force or change caused by the field
  • Calculating χ using the observed data and relevant formulas

4. What is magnetic susceptibility in MRI?

In MRI (Magnetic Resonance Imaging), magnetic susceptibility refers to how different tissues distort the local magnetic field due to their magnetic properties.

  • Differences in susceptibility can create artifacts or image distortions.
  • This is called a magnetic susceptibility artifact.

5. How does temperature affect magnetic susceptibility?

Temperature significantly affects magnetic susceptibility:

  • For paramagnetic materials, susceptibility decreases as temperature increases (Curie’s Law: χ = C/T).
  • Ferromagnetic materials lose their high susceptibility above the Curie temperature.
  • Diamagnetic materials show very little change with temperature.

6. What is the difference between magnetic susceptibility and permeability?

Magnetic susceptibility (χ) measures a material's tendency to become magnetized, while magnetic permeability (μ) indicates how easily a material allows the passage of magnetic field lines.
They are related by: μ = μ₀(1+χ), where μ₀ is the permeability of free space.

7. How are materials classified based on magnetic susceptibility?

Materials are classified as:

  • Diamagnetic (χ < 0): Slightly repelled by magnetic fields (e.g., copper, bismuth)
  • Paramagnetic (0 < χ < 1): Weakly attracted (e.g., aluminum, platinum)
  • Ferromagnetic (χ >> 1): Strongly attracted (e.g., iron, nickel)

8. What are some applications of magnetic susceptibility?

Magnetic susceptibility is widely used in:

  • Identifying minerals and ore deposits
  • Medical imaging (MRI) to detect tissue properties
  • Environmental pollution studies
  • Material science and quality testing
  • Archaeology for locating buried artifacts

9. Can magnetic susceptibility be negative? Which materials show this?

Yes, magnetic susceptibility can be negative for diamagnetic materials. These materials slightly repel magnetic fields. Examples include copper, bismuth, gold, and graphite.

10. How does iron compare to copper in terms of magnetic susceptibility?

Iron is a ferromagnetic material with very high, positive magnetic susceptibility, while copper is diamagnetic with a small negative susceptibility. Therefore, iron's susceptibility is several orders of magnitude higher than that of copper.

11. What is Curie’s Law in relation to magnetic susceptibility?

Curie’s Law states that the magnetic susceptibility (χ) of a paramagnetic material is inversely proportional to its temperature (T): χ = C/T, where C is the Curie constant. This means susceptibility decreases as temperature increases.

12. Why is understanding magnetic susceptibility important for exams like JEE/NEET/Boards?

Magnetic susceptibility is a key concept in Physics curricula and often appears in numericals, theory, and application questions in exams like JEE, NEET, and Class 12 Boards. Mastery of its definition, formulas, and applications helps secure better marks and deepens understanding of magnetism topics.