Magnetic Permeability of Different Materials: Table, Value, and Applications
Magnetic permeability is a crucial property that tells us how easily a material lets magnetic field lines pass through it. In JEE Main Physics, understanding this concept is key to solving questions on magnetic materials, solenoids, and field calculations.
The symbol for magnetic permeability is μ. Its SI unit is henry per metre (H/m). High permeability means the material supports strong magnetic field formation with less external effort, while low permeability resists it.
Materials like iron show a much greater magnetic permeability than non-magnetic materials such as copper or air. This distinction affects how devices such as transformers or inductors are designed for technological applications.
JEE Main frequently tests knowledge of permeability, its formula, and the magnetic permeability constant. For numericals, it is important to remember absolute and relative permeability, and how these play into formulae for magnetic field strength.
Magnetic Permeability: Definition and Physical Meaning
Magnetic permeability (μ) is defined as the measure of a material’s ability to allow the formation of a magnetic field within it. Physically, it describes how receptive the material is to the passage of magnetic field lines.
A high value of permeability means a material enhances the field inside it compared to the same field in air or a vacuum. This is essential to understand the behavior of materials under the influence of magnetic fields and for device engineering in electromagnetism.
The SI unit is henry per metre (H/m). The dimension is [M L T-2 A-2]. The typical symbol for permeability is μ.
Standard Value: Magnetic Permeability of Free Space (μ₀)
μ₀, pronounced as mu-naught, is the magnetic permeability of free space or vacuum. It is a physical constant used in all fundamental magnetic calculations for JEE Main.
| Constant | Symbol | Value | SI Unit |
|---|---|---|---|
| Magnetic Permeability of Free Space | μ₀ | 4π × 10-7 | H/m |
This value is fixed and frequently appears in JEE Main questions on magnetic field calculations, such as the biot-savart law and magnetic fields due to wires.
Magnetic Permeability Formula and Key Relationships
The basic relation for magnetic permeability is:
B = μH
Where B is magnetic flux density (tesla, T) and H is magnetic field strength (A/m). The proportionality constant is magnetic permeability μ.
Absolute permeability (μ) refers to the permeability of any material. Relative permeability (μr) is the ratio μ / μ₀, comparing the material’s permeability to that of free space.
Very often, JEE problems combine these ideas with magnetic moment and magnetic field calculations.
- μ = μ0 × μr
- B = μH for any medium
- B = μ0H for vacuum/air
Magnetic Permeability of Different Materials
| Material | Absolute Permeability (μ, H/m) | Relative Permeability (μr) |
|---|---|---|
| Vacuum (free space) | 4π × 10-7 | 1 |
| Air | ~4π × 10-7 | 1.0000004 |
| Copper | ~1.2566 × 10-6 | ~1 |
| Aluminum | ~1.2566 × 10-6 | ~1 |
| Water | 1.2566 × 10-6 | ~1 |
| Iron (soft) | ~6.3 × 10-3 | ~5000 |
| Steel | ~6.3 × 10-4 | ~500 |
Notice that soft iron has a dramatically higher magnetic permeability compared to copper, water, or air. For numericals, treat air and vacuum as having nearly identical μ.
- Ferromagnetic materials like iron show very high μ.
- Diamagnetic and paramagnetic materials have μ just greater or smaller than μ₀.
- Non-magnetic conductors (e.g., copper, aluminum) have μ ≈ μ₀.
Physical Significance and Applications of Magnetic Permeability
Practical uses of magnetic permeability appear in electromagnetic devices. Materials with high μ focus and guide magnetic fields, making them ideal for magnetic cores, transformers, and inductors.
- Soft iron is used in transformer cores and inductor cores due to very high μ.
- Low-μ materials like air are chosen when minimal field distortion is needed in solenoid experiments.
- Magnetic shielding in labs uses materials with calculated permeability values.
- In electromagnetic wave propagation, μ determines the speed of light in different media.
- High-μ alloys are used in magnetic field shaping for MRI and sensors.
Remember, for most JEE Main numericals, if material is not specified, assume μ = μ₀. Use appropriate values only if the question clearly mentions soft iron, steel, or other ferromagnetic materials.
Worked Example: JEE Main Type Question on Magnetic Permeability
A solenoid with 2000 turns/m carries a current of 0.2 A. If it has a soft iron core with μr = 5000, find the magnetic field inside.
- Given: n = 2000 turns/m, I = 0.2 A, μr = 5000
- B = μ₀μr nI
- μ₀ = 4π × 10-7 H/m
- B = (4π × 10-7)(5000)(2000)(0.2)
- B = 2.513 × 10-0 T (rounded)
If the core is replaced with air, μr ≈ 1 and B drops to nearly 5 × 10-4 T. This shows how dramatically magnetic permeability alters the field strength.
Revision Table: Key Facts – Magnetic Permeability
| Property | Symbol / Value | Units |
|---|---|---|
| Magnetic permeability (general) | μ | H/m |
| Magnetic permeability of free space | μ₀ = 4π × 10-7 | H/m |
| Relative permeability | μr = μ/μ₀ | dimensionless |
| Formula for field (general) | B = μH | T |
Always distinguish magnetic permeability from electrical permittivity in electromagnetism. JEE Main often plays with this contrast, so pay attention to context and symbols.
With focused revision and the right formulae, scoring on magnetic permeability questions is straightforward. For further practice and topic mastery, use Vedantu’s targeted JEE Main magnetism mock tests and explore topics like mutual inductance, magnetism revision notes, and EMI and AC revision notes to solidify your command of this essential concept.
FAQs on Magnetic Permeability: Concept, Formula, and Material Comparison
1. What is meant by magnetic permeability?
Magnetic permeability is a measure of how easily a material allows the formation of a magnetic field inside it. The higher the permeability, the better the material supports magnetic field lines.
Key facts:
- Symbol: μ
- Determines how a material responds to an applied magnetic field
- Used frequently in Physics and Engineering exams
2. What is the value of μ₀?
The magnetic permeability of free space (μ₀) is a universal constant with the value μ₀ = 4π × 10⁻⁷ H/m (henry per metre).
Quick facts:
- Also called the magnetic constant
- Essential for calculations involving magnetic fields in a vacuum or air
- Direct exam question for JEE, NEET, and CBSE Boards
3. What does a high magnetic permeability mean?
A high magnetic permeability means the material can easily allow magnetic field lines to pass through it, making it suitable for magnetic field applications.
Examples include:
- Iron and steel (used in transformer cores and electromagnets)
- Materials with high μ respond strongly to external magnetic fields
- These are important in electrical and electronic devices
4. What is permeability and its unit?
Permeability refers to a material's ability to support the formation of a magnetic field within itself. Its SI unit is henry per metre (H/m).
To remember:
- Symbol: μ
- SI unit: H/m
- Dimensionally: MLT-2A-2
5. How is magnetic permeability of air different from that of iron?
Iron has a much higher magnetic permeability compared to air, allowing it to conduct magnetic fields far more efficiently.
Comparison:
- Iron: High μ (thousands of times μ₀)
- Air: μ is almost equal to μ₀ (4π × 10⁻⁷ H/m)
- This is why iron is used in electromagnet and transformer designs
6. Where is magnetic permeability important in real life?
Magnetic permeability is crucial in many real-life applications where control or guidance of magnetic flux is essential.
Key uses:
- Transformer cores
- Electromagnets and motors
- Magnetic shielding in electronics
- Design of inductors and coils
7. What is the formula for magnetic permeability?
The standard formula for magnetic permeability (μ) is:
B = μH, where:
- B = Magnetic flux density (in tesla)
- μ = Magnetic permeability (in H/m)
- H = Magnetic field strength (in A/m)
This formula is used in calculations involving magnetic fields in different materials.
8. Is magnetic permeability the same as permittivity?
No, magnetic permeability (μ) and electric permittivity (ε) are different physical properties.
Key differences:
- Permeability (μ): Relates to magnetism and how materials support magnetic fields
- Permittivity (ε): Relates to electricity and how materials support electric fields
- Each has distinct formulas and units
9. Can magnetic permeability ever be negative?
In most natural materials, magnetic permeability is always positive. However, in certain engineered metamaterials, it can be negative, leading to unusual electromagnetic properties.
Important for exams:
- For standard JEE/NEET numericals, consider μ as positive
- Negative μ occurs in advanced physics and research materials only
10. How do you remember key values of magnetic permeability for exams?
Use quick revision tables and mnemonics to memorize key magnetic permeability values for exams.
Tips:
- μ₀ (free space): 4π × 10⁻⁷ H/m
- Air: Same as μ₀ (memorize as a default)
- Iron: Very high (approx. 1000 to 5000 × μ₀)
- Make a mini-table of common values for quick review
