Magnetism and Matter treats a bar magnet as a magnetic dipole and works out its field, the torque, potential energy and oscillations it experiences in a uniform field, then extends the idea to Earth’s magnetism described by declination, dip and the horizontal component. It also classifies all materials as diamagnetic, paramagnetic or ferromagnetic using magnetisation, magnetic intensity and susceptibility. For NEET it is a steady source of conceptual and short numerical questions and ties directly into Moving Charges and Magnetism and electromagnetic induction.
Key Concepts
1. Bar Magnet as an Equivalent Solenoid
A bar magnet behaves like a solenoid with a fixed magnetic moment. The magnetic field lines of a bar magnet are identical to those of a solenoid.
Magnetic dipole moment: m = NIA (for a solenoid/loop)
Axial field (far away): B = (μ₀/4π)(2m/r³)
Equatorial field (far away): B = (μ₀/4π)(m/r³)
2. Torque on a Magnetic Dipole
τ = m × B = mB sin θ
Potential energy: U = −m · B = −mB cos θ
3. Earth’s Magnetism
The Earth behaves like a giant bar magnet. The geographic north pole is near the magnetic south pole (field lines enter there).
Elements of Earth’s Magnetic Field
| Element | Symbol | Description |
|---|---|---|
| Declination | δ | Angle between geographic north and magnetic north at a place |
| Dip (Inclination) | I | Angle between the total magnetic field and the horizontal |
| Horizontal component | BH | BH = B cos I (component along the surface) |
Total field: B² = BH² + BV²; tan I = BV/BH
At magnetic poles: I = 90° (BH = 0); At magnetic equator: I = 0° (BV = 0)
4. Classification of Magnetic Materials
| Property | Diamagnetic | Paramagnetic | Ferromagnetic |
|---|---|---|---|
| Response to field | Weakly repelled | Weakly attracted | Strongly attracted |
| Susceptibility (χ) | Small, negative | Small, positive | Very large, positive |
| Relative permeability (μr) | Slightly < 1 | Slightly > 1 | >> 1 (10² to 10⁵) |
| Examples | Bismuth, copper, diamond, water | Aluminium, sodium, oxygen, platinum | Iron, cobalt, nickel, gadolinium |
| Temperature effect | Independent | χ ∝ 1/T (Curie’s law) | Above Curie temp → paramagnetic |
Key Terms
- Magnetisation (M): Magnetic moment per unit volume; M = χH
- Magnetic susceptibility (χ): Measures how easily a material is magnetised
- Magnetic permeability (μ): μ = μ₀(1 + χ) = μ₀μr
- Curie temperature: Temperature above which ferromagnetic becomes paramagnetic
- Hysteresis: Lagging of B behind H when a ferromagnet is magnetised and demagnetised
Hysteresis Loop
- Retentivity: B remaining when H is reduced to zero
- Coercivity: Reverse H needed to reduce B to zero
- Area of hysteresis loop = energy lost per cycle
- Soft iron: narrow loop (electromagnets, transformers)
- Steel: wide loop (permanent magnets)
Important Definitions
| Term | Definition |
|---|---|
| Magnetic dipole moment | m = NIA - product of current, area, and number of turns |
| Declination | Angle between geographic and magnetic meridians at a place |
| Dip | Angle of Earth’s field with horizontal |
| Diamagnetic | Materials weakly repelled by magnets (χ < 0) |
| Paramagnetic | Materials weakly attracted by magnets (χ > 0, small) |
| Ferromagnetic | Materials strongly attracted by magnets (χ >> 0) |
| Curie temperature | Temperature above which ferromagnets lose their ferromagnetism |
| Hysteresis | Lagging of magnetisation behind the applied field in ferromagnets |
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Solved Examples
Example 1
At a place, BH = 0.3 G and dip angle = 60°. Find the total magnetic field.
Answer: BH = B cos I → B = BH/cos I = 0.3/cos 60° = 0.3/0.5 = 0.6 G
Example 2
A bar magnet of magnetic moment 0.5 A·m² is placed at 30° to a uniform field of 0.2 T. Find the torque.
Answer: τ = mB sin θ = 0.5 × 0.2 × sin 30° = 0.1 × 0.5 = 0.05 N·m
Important Questions for Board Exams
1-Mark
- Define magnetic declination.
- What is the Curie temperature?
3-Mark
- Classify magnetic materials into three categories. Give properties and examples of each.
- Define the three elements of Earth’s magnetic field. How are they related?
- What is a hysteresis loop? What do retentivity and coercivity represent?
5-Mark
- Distinguish between diamagnetic, paramagnetic, and ferromagnetic materials with examples. Explain the concept of Curie temperature and hysteresis.
Quick Revision Points
- Bar magnet ≈ magnetic dipole; m = NIA; τ = mB sin θ; U = −mB cos θ
- Earth’s field: Declination (δ), Dip (I), Horizontal component BH = B cos I
- Diamagnetic: χ < 0, repelled (Cu, Bi, H₂O); Paramagnetic: χ > 0, weak attraction (Al, O₂)
- Ferromagnetic: χ >> 0, strong attraction (Fe, Co, Ni); above Curie temp → paramagnetic
- Curie’s law (paramagnetic): χ ∝ 1/T
- Hysteresis: retentivity (B at H=0), coercivity (H to make B=0)
- Soft iron: easy to magnetise/demagnetise (electromagnets); Steel: permanent magnets
Previous: Ch 4 - Moving Charges and Magnetism
Next: Ch 6 - Electromagnetic Induction
Class 12 Physics · Chapter 5 – swipe through all 8 cards to understand the whole chapter.
Bar Magnet as a Magnetic Dipole
A bar magnet is two equal-and-opposite poles, behaving exactly like a magnetic dipole.
2l is the magnetic length (~0.84 of geometric length); moment points S → N.
- Pole strength m_pole has unit A·m; moment m has unit A·m2
- No magnetic monopoles — cutting a magnet gives two smaller dipoles
- Equivalent to a solenoid: m = N I A; field lines are closed loops
Field of a Magnetic Dipole
Reuse electric-dipole results by swapping p → m and 1/(4πε0) → μ0/4π.
Valid for a short magnet (r ≫ size); μ0/4π = 10⁻7 T·m/A.
- Axial field is twice the equatorial: B_axial = 2 B_equator
- Axial B is along m; equatorial B is opposite to m
- Both fall off as 1/r3 — the dipole signature
Torque on a Dipole
A uniform field can’t pull a dipole, but it twists it toward alignment.
Net force is zero in a uniform field — only torque acts.
- Maximum τ = mB at θ = 90°
- τ = 0 at θ = 0° (stable) and θ = 180° (unstable)
- A net translational force needs a non-uniform field
Potential Energy of a Dipole
Aligning with the field is the relaxed, low-energy state; opposing it costs energy.
Work to rotate θ1 → θ2 is W = mB(cosθ1 − cosθ2).
- Minimum U = −mB at θ = 0° (stable equilibrium)
- Maximum U = +mB at θ = 180° (unstable)
- U = 0 at θ = 90° (dipole perpendicular to field)
Oscillations in a Field
A magnet nudged from alignment swings like a torsional pendulum.
I is the moment of inertia; used to compare B or m experimentally.
- Period depends on inertia I, moment m and field B
- Stronger field or larger moment → faster oscillation
- Standard NEET method to find m or compare field strengths
Earth’s Magnetism
Earth acts like a giant tilted bar magnet, fixed by three field elements.
Magnetic S-pole lies near geographic North; axis tilted ~11.3°.
- Three elements: Declination D, Dip/Inclination I, Horizontal component B_H
- Magnetic equator: I = 0° → field horizontal, B_V = 0
- Magnetic poles: I = 90° → field vertical, B_H = 0; B_E = √(B_H2 + B_V2)
Magnetisation, H & Susceptibility
Inside matter, the applied field, the material’s response and the total field stay separate.
H and M share the unit A/m; χ and μᵣ are dimensionless; μ = μ0μᵣ.
- H = applied magnetising field, M = magnetisation (moment per volume)
- χ small negative → dia; small positive → para; large positive → ferro
- μᵣ < 1 (dia), slightly > 1 (para), ≫ 1 (ferro)
Dia, Para & Ferromagnetism
Bring a magnet near a material: repelled, weakly pulled, or fiercely pulled sorts all matter.
Memory hook: Dia = away, Para = pulled, Ferro = fiercely pulled.
- Diamagnetic (Bi, Cu, water): χ < 0, temp-independent; superconductor χ = −1
- Paramagnetic (Al, Na, O2): χ small +, obeys Curie’s law χ = C/T
- Ferromagnetic (Fe, Co, Ni): χ ≫ 0, domains & hysteresis; → paramagnetic above T_c
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Related Chapters in Class 12 Physics
- Moving Charges and Magnetism Class 12 Notes
- Electromagnetic Induction Class 12 Notes
- Current Electricity Class 12 Notes
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Frequently Asked Questions
A magnetic dipole is a pair of equal and opposite magnetic poles separated by a small distance, and a bar magnet behaves exactly like one. Its magnetic moment m equals pole strength times the magnetic length 2l, has unit ampere metre squared, and points from the south pole to the north pole.
On the axial line the field is B = (mu0 / 4pi) times 2m / r cubed, and on the equatorial line it is B = (mu0 / 4pi) times m / r cubed, so the axial field is twice the equatorial field. Both fall off as 1 over r cubed, which is the signature of a dipole.
The torque is tau = mB sin theta, which is maximum at 90 degrees and zero when the dipole is aligned or anti-aligned with the field. The potential energy is U = minus mB cos theta, minimum at 0 degrees (stable equilibrium) and maximum at 180 degrees (unstable).
Diamagnetic materials (like bismuth and copper) have a small negative susceptibility and are weakly repelled, paramagnetic materials (like aluminium and oxygen) have a small positive susceptibility and are weakly attracted and obey Curie’s law, and ferromagnetic materials (like iron, cobalt and nickel) have a very large positive susceptibility, show domains and hysteresis, and become paramagnetic above the Curie temperature.
Yes, it is part of the Class 12 NEET physics syllabus and usually contributes one question, mostly conceptual or short numerical, on torque, potential energy, Earth’s magnetic elements, or the dia, para and ferro classification. It is best prepared together with Moving Charges and Magnetism.