🧲 Magnetism and Matter 🧲
📖 Welcome to Magnetism and Matter Class 12 Notes
Master Magnetism and Matter Class 12 Physics Chapter 5 with complete notes covering bar magnet magnetic field, magnetic dipole moment, Gauss's law for magnetism, magnetisation and magnetic intensity, and all magnetic properties of materials. This chapter explores how matter responds to magnetic fields - from diamagnetism and paramagnetism to ferromagnetism Class 12. Perfect for NCERT CBSE RBSE board exams and competitive preparation (JEE Main, JEE Advanced, NEET 2025).
📊 Chapter 5 Quick Summary
NCERT Reference: Class 12 Physics Part 1, Chapter 5 - Magnetism and Matter
Moderate
12-15 hours
8+ Complete
15+ Solved
6-10 marks
Medium-High
📑 Complete Chapter Contents (Click to Jump)
1. Introduction to Magnetism and Matter
While Chapter 4 dealt with how moving charges produce magnetic fields, this chapter explores how matter itself responds to magnetic fields. Every material, when placed in a magnetic field, gets magnetized to some extent - though the nature and strength of this magnetization varies dramatically.
1.1 Historical Context
The study of magnetism dates back to ancient civilizations who observed that certain naturally occurring stones (magnetite, Fe₃O₄) attracted iron. The Chinese used magnetic compasses for navigation as early as 1100 CE. However, the scientific understanding of magnetism in matter came much later.
| Year | Scientist | Discovery |
|---|---|---|
| 1269 | Pierre de Maricourt | Poles of magnet, like poles repel |
| 1600 | William Gilbert | Earth behaves like giant magnet |
| 1820 | Hans Christian Ørsted | Connection between electricity & magnetism |
| 1845 | Michael Faraday | Diamagnetism discovered |
| 1895 | Pierre Curie | Temperature effect on ferromagnetism |
1.2 Scope of This Chapter
In this comprehensive guide to Magnetism and Matter Class 12, you will learn:
- Properties and behavior of bar magnets
- Concept of magnetic dipole and its analog to electric dipole
- Gauss's law for magnetism and why magnetic monopoles don't exist
- How materials get magnetized (magnetisation and magnetic intensity)
- Three fundamental types of magnetic behavior: diamagnetism, paramagnetism, and ferromagnetism
- Practical applications: magnetic storage, MRI, transformers, electromagnets
🔬 Why This Chapter Matters
Academic Importance:
- Board Exams: 6-10 marks typically from this chapter
- JEE Main: Magnetic properties, bar magnet concepts (2-3 questions)
- NEET: Conceptual questions on types of magnetism
Real-World Applications:
- Data Storage: Hard disks use ferromagnetic materials
- Medical: MRI machines utilize nuclear magnetic resonance
- Electronics: Transformers, inductors use magnetic cores
- Separation: Magnetic separation in industries
2. The Bar Magnet - Fundamental Properties
A bar magnet is a permanent magnet in the shape of a rectangular bar. It is the simplest and most common form of magnet, serving as an excellent model to understand magnetic phenomena.
2.1 Basic Properties of Bar Magnet
📌 Key Properties
- Two Poles: Every magnet has two poles - North (N) and South (S)
- Poles Cannot Be Separated: If you break a magnet, each piece becomes a new magnet with both poles
- Attractive and Repulsive Forces:
- Like poles repel (N-N or S-S)
- Unlike poles attract (N-S)
- Directive Property: A freely suspended magnet aligns itself in North-South direction
- Strongest at Poles: Magnetic strength is maximum at the two ends
Shows rectangular bar magnet with North and South poles labeled, magnetic field lines emerging from N and entering S
2.2 Magnetic Dipole Moment
A bar magnet can be modeled as a magnetic dipole - analogous to an electric dipole but with magnetic poles instead of charges.
Or simply: $$m = \text{pole strength} \times \text{magnetic length}$$
Where:
- m = magnetic dipole moment (A·m²)
- m = pole strength (A·m)
- 2l = magnetic length (distance between poles)
Direction: From South pole to North pole (inside the magnet)
⚠️ Important Distinction
Magnetic Length vs Geometric Length:
The magnetic length (2l) is slightly less than the actual geometric length of the bar magnet because the poles are not exactly at the ends but slightly inside.
Typically: Magnetic length ≈ 0.84 × Geometric length
2.3 Pole Strength
The pole strength (denoted by q_m or m) is a measure of the strength of a magnetic pole.
- Unit: Ampere-meter (A·m) in SI system
- Nature: Scalar quantity (but can be positive or negative)
- Convention: North pole: +q_m, South pole: −q_m
📌 Note on Pole Strength
Unlike electric charge, isolated magnetic poles do not exist. Pole strength is a useful mathematical concept but physically, poles always come in pairs (dipole).
3. Magnetic Field Lines of a Bar Magnet
Magnetic field lines are imaginary lines used to represent the magnetic field around a magnet. They provide a visual way to understand the direction and relative strength of the magnetic field.
3.1 Properties of Magnetic Field Lines
| Property | Description |
|---|---|
| Origin & Termination | Outside magnet: N → S Inside magnet: S → N (forming closed loops) |
| Direction | Tangent to field line gives direction of magnetic field at that point |
| Density | Closer lines indicate stronger field |
| Never Intersect | Two field lines never cross each other |
| Closed Loops | Always form closed loops (unlike electric field lines) |
| Weakest Point | At the center of bar magnet (equator) |
Shows field lines emerging from North pole, curving around, and entering South pole, with lines continuing inside from S to N
3.2 Key Observations
🎯 Understanding Field Line Patterns
1. Closed Loop Nature:
Magnetic field lines always form closed loops. This is fundamentally different from electric field lines which start on positive charges and end on negative charges. The closed-loop nature reflects the fact that magnetic monopoles do not exist.
2. Direction Convention:
By convention, field lines are drawn from North to South outside the magnet. However, to complete the loop, they must continue from South to North inside the magnet.
3. Field Strength Indication:
The density of field lines indicates field strength. Near the poles, lines are densely packed (strong field). At the equator (center), lines are sparse (weak field).
3.3 Comparison with Electric Field Lines
| Property | Electric Field Lines | Magnetic Field Lines |
|---|---|---|
| Origin | Start from positive charge | Emerge from N pole (by convention) |
| Termination | End at negative charge | Enter S pole (by convention) |
| Nature | Open curves (can start/end at infinity) | Always closed loops |
| Source | Electric charges (monopoles exist) | Magnetic dipoles (monopoles don't exist) |
| Inside Source | Can be zero (hollow conductor) | Never zero (lines continue inside) |
⚠️ Common Mistake Students Make
WRONG: "Magnetic field lines start from North pole and end at South pole."
CORRECT: "Magnetic field lines emerge from North pole and enter South pole outside the magnet, but continue from S to N inside the magnet, forming closed loops."
🎯 Remember: Magnetic field lines NEVER begin or end - they always form closed loops!
4. Bar Magnet as an Equivalent Solenoid
A remarkable discovery in magnetism is that a bar magnet behaves exactly like a solenoid (current-carrying coil) in terms of the magnetic field it produces.
4.1 The Equivalence
📌 Key Concept
The magnetic field pattern around a bar magnet is identical to that around a solenoid carrying current. This suggests that magnetism in materials arises from circulating currents at the atomic level.
Shows bar magnet on left with N-S poles and field lines, solenoid on right with current direction and identical field pattern
4.2 Physical Explanation
The equivalence arises because:
- Atomic Current Loops: Electrons orbiting nuclei act like tiny current loops
- Electron Spin: Intrinsic spin of electrons creates additional magnetic moments
- Alignment: In a magnetized material, these atomic magnetic moments align
- Net Effect: Aligned atomic currents produce a field similar to a solenoid
🔬 Qualitative Understanding (As per NCERT)
The NCERT syllabus requires only qualitative understanding of this equivalence. The key takeaway is:
"All magnetic phenomena can be explained in terms of circulating currents."
This is the basis of Ampère's Molecular Current Hypothesis - that magnetism in materials is due to microscopic current loops within atoms.
4.3 Implications
This equivalence tells us:
- There are no magnetic charges (monopoles) - only circulating currents
- Magnetism is fundamentally an electromagnetic phenomenon
- Breaking a magnet creates two magnets because you cannot separate current loops
5. Magnetic Dipole in a Uniform Magnetic Field
When a magnetic dipole (like a bar magnet) is placed in a uniform external magnetic field, it experiences both a torque and a force (if the field is non-uniform).
5.1 Torque on Magnetic Dipole
📐 Derivation: Torque on Dipole
Consider: Magnetic dipole of moment m with poles of strength ±q_m separated by distance 2l, placed in uniform field B at angle θ.
Forces on poles:
Force on N-pole: F = q_m B (along field)
Force on S-pole: F = q_m B (opposite to field)
These forces form a couple:
Perpendicular distance between forces = 2l sin θ
Torque = Force × Perpendicular distance
$$\\tau = q_m B \\times 2l \\sin\\theta$$
$$\\tau = (q_m \\times 2l) B \\sin\\theta$$
$$\\tau = mB\\sin\\theta$$
Vector form: $$\\vec{\\tau} = \\vec{m} \\times \\vec{B}$$
Where:
- m = magnetic dipole moment
- B = magnetic field strength
- θ = angle between m and B
5.2 Potential Energy of Magnetic Dipole
The potential energy of a magnetic dipole in an external field depends on its orientation.
📐 Derivation: Potential Energy
Work done in rotating dipole from angle θ₁ to θ₂:
$$W = \\int_{\\theta_1}^{\\theta_2} \\tau \\, d\\theta = \\int_{\\theta_1}^{\\theta_2} mB\\sin\\theta \\, d\\theta$$
$$W = mB[-\\cos\\theta]_{\\theta_1}^{\\theta_2} = mB(\\cos\\theta_1 - \\cos\\theta_2)$$
Taking reference (U = 0) at θ = 90°:
$$U = -mB\\cos\\theta$$
Vector form: $$U = -\\vec{m} \\cdot \\vec{B}$$
Special cases:
- θ = 0° (m ∥ B): U = −mB (minimum, stable)
- θ = 90° (m ⊥ B): U = 0 (reference)
- θ = 180° (m anti-parallel to B): U = +mB (maximum, unstable)
5.3 Equilibrium Positions
| Position | θ | Torque | Energy | Stability |
|---|---|---|---|---|
| Parallel to B | 0° | 0 | −mB (min) | Stable |
| Perpendicular to B | 90° | mB (max) | 0 | Unstable |
| Antiparallel to B | 180° | 0 | +mB (max) | Unstable |
Problem: A bar magnet of magnetic moment 2.0 A·m² is placed in a uniform field of 0.5 T at an angle of 60° with the field. Calculate (a) torque (b) potential energy.
Given: m = 2.0 A·m², B = 0.5 T, θ = 60°
(a) Torque:
$$\\tau = mB\\sin\\theta = (2.0)(0.5)\\sin 60°$$
$$\\tau = 1.0 \\times 0.866 = 0.866 \\text{ N·m}$$
(b) Potential Energy:
$$U = -mB\\cos\\theta = -(2.0)(0.5)\\cos 60°$$
$$U = -1.0 \\times 0.5 = -0.5 \\text{ J}$$
Answers: (a) τ = 0.866 N·m, (b) U = −0.5 J
📌 Understanding Magnetic Length (0.84 Factor)
Why do we multiply by 0.84?
The magnetic length of a bar magnet is slightly less than its geometric (physical) length because the magnetic poles are not located exactly at the ends, but slightly inside.
Key Facts:
- Geometric Length: Physical length measured with ruler
- Magnetic Length (2l): Effective distance ≈ 0.84 × Geometric length
- Board Exam: Use 2l = 0.84 × L unless specified otherwise
- NCERT Standard: Experimentally determined value
⚠️ Exam Alert: Read carefully whether question says "geometric" or "magnetic" length!
📝 Board Exam Tip: Torque & Potential Energy
Most Common Numerical Problem:
"A bar magnet of moment m is placed at angle θ in field B. Calculate (a) torque (b) potential energy."
Quick Answer Template:
- Write formulas: τ = mB sin θ and U = -mB cos θ
- Substitute given values
- Calculate and write units
- State stable/unstable equilibrium if asked
6. The Electrostatic Analog
There is a beautiful mathematical analogy between electric dipoles and magnetic dipoles. This analog helps us understand magnetic phenomena using our knowledge of electrostatics.
6.1 Comparison Table
| Property | Electric Dipole | Magnetic Dipole |
|---|---|---|
| Basic Entity | Electric charges (±q) | Magnetic poles (±q_m) |
| Dipole Moment | $$\\vec{p} = q\\vec{d}$$ | $$\\vec{m} = q_m(2\\vec{l})$$ |
| Torque in Field | $$\\vec{\\tau} = \\vec{p} \\times \\vec{E}$$ | $$\\vec{\\tau} = \\vec{m} \\times \\vec{B}$$ |
| Potential Energy | $$U = -\\vec{p} \\cdot \\vec{E}$$ | $$U = -\\vec{m} \\cdot \\vec{B}$$ |
| Field at Axial Point | $$E = \\frac{2p}{4\\pi\\epsilon_0 r^3}$$ | $$B = \\frac{\\mu_0 m}{2\\pi r^3}$$ |
| Field at Equatorial Point | $$E = \\frac{p}{4\\pi\\epsilon_0 r^3}$$ | $$B = \\frac{\\mu_0 m}{4\\pi r^3}$$ |
| Isolated Entity | Exists (monopoles) | Does NOT exist |
⚠️ Critical Difference
Electric monopoles (isolated charges) exist, but magnetic monopoles do NOT exist.
You can have a single positive or negative charge, but you cannot have an isolated north or south pole. Every magnet must have both poles.
6.2 Mathematical Correspondence
The analog allows us to write corresponding equations by making substitutions:
| Electric Quantity | ↔ | Magnetic Quantity |
|---|---|---|
| Electric charge (q) | ↔ | Pole strength (q_m) |
| Electric dipole moment (p) | ↔ | Magnetic dipole moment (m) |
| Electric field (E) | ↔ | Magnetic field (B) |
| $$\\frac{1}{4\\pi\\epsilon_0}$$ | ↔ | $$\\frac{\\mu_0}{4\\pi}$$ |
7. Gauss's Law for Magnetism
Gauss's law for magnetism is one of Maxwell's four fundamental equations of electromagnetism. It mathematically expresses the non-existence of magnetic monopoles.
7.1 Statement
In words:
The net magnetic flux through any closed surface is always zero.
7.2 Physical Meaning
🔬 What This Means
1. No Magnetic Monopoles:
The zero flux means that the number of field lines entering a closed surface equals the number leaving it. This implies magnetic field lines never begin or end - they always form closed loops.
2. Contrast with Electric Gauss's Law:
Electric Gauss's law: $$\\oint \\vec{E} \\cdot d\\vec{A} = \\frac{Q_{enclosed}}{\\epsilon_0}$$
This can be non-zero because electric charges (monopoles) exist. Magnetic Gauss's law is always zero because magnetic monopoles don't exist.
3. Indivisibility of Poles:
If you enclose just the north pole of a magnet in a surface, an equal amount of flux enters through the south pole (which must be inside or cutting through the surface), making net flux zero.
Shows closed surface around bar magnet with equal number of field lines entering and leaving
7.3 Consequences
- Magnetic Field Lines: Always form closed loops (no beginning or end)
- Cutting a Magnet: Always produces two complete magnets, never isolated poles
- Magnetic Charges: Do not exist in nature
Question: A bar magnet is enclosed completely inside a closed surface. What is the net magnetic flux through the surface?
Solution:
By Gauss's law for magnetism: $$\\oint \\vec{B} \\cdot d\\vec{A} = 0$$
The net magnetic flux is zero regardless of:
- Size or shape of the closed surface
- Strength of the magnet
- Position of magnet inside the surface
Answer: Net magnetic flux = 0
Reason: Every field line that emerges from the surface (from N pole) must re-enter (at S pole), making net flux zero.
📝 Board Exam Tip: Gauss's Law for Magnetism
Most Asked Question Format:
"State Gauss's law for magnetism. Why is the net magnetic flux through a closed surface always zero?"
Perfect Answer Strategy:
- State the law: ∮B⃗·dA⃗ = 0 (write formula first)
- Explain: Net magnetic flux = 0 because field lines form closed loops
- Reason: Magnetic monopoles don't exist in nature
- Contrast: Unlike electric charges which can exist independently
8. Magnetisation and Magnetic Intensity
When a material is placed in an external magnetic field, it becomes magnetized. Two important quantities describe this magnetization.
8.1 Magnetisation (M) - Intensity of Magnetisation
Magnetisation (M) describes how magnetized a material becomes when placed in a magnetic field.
$$M = \\frac{m_{net}}{V}$$
Unit: A/m (ampere per meter)
Nature: Vector quantity (direction = direction of net magnetic moment)
Physical Meaning: Magnetisation represents the magnetic dipole moment per unit volume of the material.
8.2 Magnetic Intensity (H)
Magnetic intensity (H), also called magnetising field, is the part of the magnetic field that depends only on external currents, not on the magnetization of the material.
Or equivalently: $$\\vec{B} = \\mu_0(\\vec{H} + \\vec{M})$$
Unit: A/m (ampere per meter)
Nature: Vector quantity
Physical Meaning: H is the "applied" magnetic field, while B is the "total" magnetic field (applied + induced).
8.3 Magnetic Susceptibility (χ_m)
Magnetic susceptibility measures how easily a material can be magnetized.
Or: $$\\vec{M} = \\chi_m \\vec{H}$$
Unit: Dimensionless (unitless)
Nature: Can be positive or negative depending on material type
8.4 Relative Permeability (μ_r)
Also: $$\\mu = \\mu_r \\mu_0$$
where μ = absolute permeability of material
8.5 Relationship Between B, H, and M
📌 Key Relationships
$$\\vec{B} = \\mu_0(\\vec{H} + \\vec{M})$$
$$\\vec{M} = \\chi_m \\vec{H}$$
$$\\vec{B} = \\mu_0(1 + \\chi_m)\\vec{H} = \\mu_0 \\mu_r \\vec{H}$$
$$\\vec{B} = \\mu \\vec{H}$$
9. Diamagnetism
Diamagnetism is a weak form of magnetism exhibited by all materials. It arises from the orbital motion of electrons and opposes the applied magnetic field.
9.1 Properties of Diamagnetic Materials
| Property | Value/Description |
|---|---|
| Susceptibility (χ_m) | Small and negative (−10⁻⁵ to −10⁻⁹) |
| Relative Permeability (μ_r) | Slightly less than 1 (μ_r < 1) |
| Behavior in Field | Repelled by magnets (weakly) |
| Field Lines | Expelled from material |
| Temperature Dependence | Independent of temperature |
| Presence | Present in ALL materials (usually masked by stronger effects) |
9.2 Origin of Diamagnetism
🔬 Physical Mechanism
1. Lenz's Law Manifestation:
When an external field is applied, it induces orbital currents in atoms that oppose the applied field (analogous to Lenz's law in electromagnetic induction).
2. Electron Orbital Motion:
The applied field changes the angular velocity of orbiting electrons, creating a magnetic moment that opposes the field.
3. Universal Property:
All materials have diamagnetic response, but it's usually very weak and masked by stronger para- or ferromagnetic effects.
9.3 Examples of Diamagnetic Materials
- Elements: Bismuth (Bi), Copper (Cu), Gold (Au), Silver (Ag)
- Compounds: Water (H₂O), Sodium Chloride (NaCl), Benzene
- Inert Gases: Helium, Neon, Argon
- Special: Superconductors (perfect diamagnetism, χ_m = −1)
📌 Interesting Fact
Superconductors are perfect diamagnets with χ_m = −1. They completely expel magnetic fields from their interior (Meissner effect), which allows for magnetic levitation.
Shows field lines being pushed away from diamagnetic material
10. Paramagnetism
Paramagnetism is a form of magnetism where materials are weakly attracted to magnetic fields. It occurs in materials with unpaired electrons.
10.1 Properties of Paramagnetic Materials
| Property | Value/Description |
|---|---|
| Susceptibility (χ_m) | Small and positive (10⁻⁵ to 10⁻³) |
| Relative Permeability (μ_r) | Slightly greater than 1 (μ_r > 1) |
| Behavior in Field | Attracted by magnets (weakly) |
| Field Lines | Slightly concentrated in material |
| Temperature Dependence | Inversely proportional to temperature (Curie's Law) |
| Presence | In materials with unpaired electrons |
10.2 Origin of Paramagnetism
🔬 Physical Mechanism
1. Permanent Atomic Magnetic Moments:
Atoms/molecules with unpaired electrons have permanent magnetic moments due to electron spin and orbital angular momentum.
2. Random Orientation (No Field):
Without external field, these moments are randomly oriented due to thermal agitation → no net magnetization.
3. Partial Alignment (With Field):
External field tries to align moments parallel to field, but thermal agitation opposes this → weak net magnetization in field direction.
4. Temperature Effect:
Higher temperature → more thermal agitation → less alignment → weaker magnetization.
10.3 Curie's Law
For paramagnetic materials, susceptibility varies inversely with absolute temperature:
Where:
- C = Curie constant (material-specific)
- T = Absolute temperature (K)
Implication: Paramagnetism weakens as temperature increases
10.4 Examples of Paramagnetic Materials
- Elements: Aluminum (Al), Platinum (Pt), Chromium (Cr), Manganese (Mn)
- Oxygen (O₂): Liquid oxygen is paramagnetic
- Compounds: CuSO₄, MnSO₄, CuCl₂
- Ions: Most transition metal ions (Fe³⁺, Cu²⁺, Cr³⁺)
Shows atomic magnetic moments partially aligned with applied field
11. Ferromagnetism
Ferromagnetism is the strongest form of magnetism. Ferromagnetic materials can be permanently magnetized and show strong attraction to magnets.
11.1 Properties of Ferromagnetic Materials
| Property | Value/Description |
|---|---|
| Susceptibility (χ_m) | Very large and positive (10³ to 10⁵) |
| Relative Permeability (μ_r) | Very large (10² to 10⁵) |
| Behavior in Field | Strongly attracted by magnets |
| Field Lines | Highly concentrated in material |
| Magnetization | Can be permanent (retentivity) |
| Temperature Dependence | Loses ferromagnetism above Curie temperature (T_c) |
| Hysteresis | Shows hysteresis (magnetization lags behind field) |
11.2 Origin of Ferromagnetism - Domain Theory
🔬 Physical Mechanism - Magnetic Domains
1. Spontaneous Magnetization:
In ferromagnetic materials, there exist small regions called magnetic domains (~ 1 mm size) within which all atomic magnetic moments are naturally aligned parallel (even without external field).
2. Random Domain Orientation (Unmagnetized):
In an unmagnetized ferromagnetic sample, domains point in random directions → no net magnetization.
3. Domain Alignment (Magnetization Process):
When external field is applied:
- Stage 1: Domains aligned with field grow at expense of others
- Stage 2: Domains rotate to align with field
- Result: Strong net magnetization
4. Permanent Magnetism:
Even after removing external field, domains remain partially aligned → material retains magnetization (permanent magnet).
Shows random domain orientation changing to aligned orientation
11.3 Curie Temperature (T_c)
Above a certain temperature called Curie temperature, ferromagnetic materials lose their ferromagnetism and become paramagnetic.
Definition: Temperature above which ferromagnetic → paramagnetic transition occurs
Reason: Thermal agitation at high temperature destroys the domain structure
Above T_c: Material obeys Curie-Weiss law
11.4 Curie Temperatures of Common Ferromagnets
| Material | Curie Temperature (T_c) |
|---|---|
| Iron (Fe) | 1043 K (770°C) |
| Cobalt (Co) | 1394 K (1121°C) |
| Nickel (Ni) | 631 K (358°C) |
| Gadolinium (Gd) | 293 K (20°C) |
11.5 Examples of Ferromagnetic Materials
- Pure Metals: Iron (Fe), Cobalt (Co), Nickel (Ni), Gadolinium (Gd)
- Alloys: Steel, Alnico, Permalloy
- Compounds: Fe₃O₄ (magnetite), CrO₂ (chromium dioxide)
- Rare Earths: Neodymium magnets (Nd₂Fe₁₄B) - strongest permanent magnets
11.6 Hysteresis
Hysteresis is the phenomenon where magnetization (M) lags behind the magnetizing field (H).
📌 Hysteresis Loop
Key Points on B-H Curve:
- Retentivity (B_r): Magnetization remaining when H = 0
- Coercivity (H_c): Reverse field needed to reduce B to zero
- Saturation: Point beyond which B doesn't increase with H
Energy Loss: Area enclosed by hysteresis loop = energy dissipated per cycle as heat
Shows characteristic S-shaped loop with labeled retentivity and coercivity points
11.7 Applications of Ferromagnetism
| Application | Material Used | Property Utilized |
|---|---|---|
| Permanent Magnets | Alnico, Neodymium | High retentivity, high coercivity |
| Transformer Cores | Soft iron, Silicon steel | High permeability, low hysteresis loss |
| Magnetic Recording | CrO₂, Fe₂O₃ | Moderate coercivity |
| Electromagnets | Soft iron | High permeability, low retentivity |
📊 Previous Year Question Trend: Magnetic Materials
High-Frequency Topics (CBSE/RBSE 2022-2025):
- 2024 CBSE: Define Curie temperature (1 mark) - Very common!
- 2023 RBSE: Compare dia/para/ferro with examples (3 marks)
- 2022 CBSE: Hysteresis curve explanation (2 marks)
🎯 High Probability for 2026: Comparison table of three magnetic materials - Prepare thoroughly!
Comparison of Magnetic Materials
| Property | Diamagnetic | Paramagnetic | Ferromagnetic |
|---|---|---|---|
| χ_m | Negative (−10⁻⁹ to −10⁻⁵) | Positive & Small (10⁻⁵ to 10⁻³) | Positive & Large (10³ to 10⁵) |
| μ_r | μ_r < 1 | μ_r > 1 (slightly) | μ_r >> 1 |
| Behavior | Repelled (weakly) | Attracted (weakly) | Attracted (strongly) |
| Temp Effect | Independent | χ_m ∝ 1/T | Above T_c: paramagnetic |
| Field Lines | Expelled | Slightly concentrated | Highly concentrated |
| Permanence | No | No | Yes (retentivity) |
| Origin | Induced moments (Lenz) | Partial alignment | Domain alignment |
| Examples | Bi, Cu, H₂O | Al, Pt, O₂ | Fe, Co, Ni |
📊 Numerical Problem Trend
High-Frequency Calculation Types:
- Type 1: Given χ_m, find μ_r (Very Easy - appears every year)
- Type 2: Magnetic moment from pole strength (Medium - 70% papers)
- Type 3: Torque/PE with angle (Hard - 50% papers, 3 marks)
🎯 Pro Tip: Practice Type 3 problems - they carry maximum marks and test derivation understanding!
📐 Complete Formula Sheet
Bar Magnet & Dipole
| Quantity | Formula |
|---|---|
| Magnetic Dipole Moment | m = q_m × 2l |
| Torque on Dipole | τ = mB sin θ or τ⃗ = m⃗ × B⃗ |
| Potential Energy | U = −mB cos θ or U = −m⃗ · B⃗ |
| Magnetic Length | ≈ 0.84 × Geometric length |
Magnetic Field of Bar Magnet
| Location | Formula |
|---|---|
| Axial (end-on) | $$B = \\frac{\\mu_0}{4\\pi} \\frac{2m}{r^3}$$ |
| Equatorial (broadside-on) | $$B = \\frac{\\mu_0}{4\\pi} \\frac{m}{r^3}$$ |
Magnetisation & Intensity
| Quantity | Formula |
|---|---|
| Magnetisation | M = m_net/V |
| Magnetic Intensity | H⃗ = B⃗/μ₀ − M⃗ |
| Relationship | B⃗ = μ₀(H⃗ + M⃗) |
| Susceptibility | χ_m = M/H |
| Relative Permeability | μ_r = 1 + χ_m |
| Permeability | μ = μ_r μ₀ or B = μH |
Temperature Laws
| Law | Formula | Material |
|---|---|---|
| Curie's Law | χ_m = C/T | Paramagnetic |
| Curie-Weiss Law | χ_m = C/(T − T_c) | Ferromagnetic (T > T_c) |
Important Constants
| Constant | Value |
|---|---|
| μ₀ (Permeability of free space) | 4π × 10⁻⁷ T·m/A |
| μ₀/4π | 10⁻⁷ T·m/A |
❓ Multiple Choice Questions
Note: Practice more questions from NCERT exercises and previous year papers for board exam preparation.
📘 Solved Numerical Problems
Problem: A bar magnet of length 10 cm has pole strength 5 A·m. Calculate its magnetic moment.
Given: Geometric length = 10 cm, q_m = 5 A·m
Magnetic length: 2l = 0.84 × 10 = 8.4 cm = 0.084 m
m = q_m × 2l = 5 × 0.084 = 0.42 A·m²
Answer: m = 0.42 A·m²
Problem: A material has magnetic susceptibility χ_m = 2.5 × 10⁻⁵. Find its relative permeability.
Given: χ_m = 2.5 × 10⁻⁵
μ_r = 1 + χ_m = 1 + 2.5 × 10⁻⁵ = 1.000025
Answer: μ_r = 1.000025 (slightly paramagnetic)
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