Magnetism and Matter
'The Earth is a giant magnet — and every piece of iron is a collection of tiny magnets waiting to align.'
1. Chapter Overview
This chapter explores magnetism beyond current-carrying wires — in MATERIALS. Topics include: the BAR MAGNET (magnetic dipole, field lines, torque in a uniform field), the EARTH'S MAGNETISM (magnetic declination, dip, horizontal component), MAGNETISATION AND INTENSITY, three types of MAGNETIC MATERIALS (diamagnetic, paramagnetic, ferromagnetic), and HYSTERESIS.
2. Bar Magnet as a Magnetic Dipole
- A bar magnet has a NORTH pole (magnetic moment towards) and SOUTH pole (away).
- Magnetic dipole moment m = q_m × 2l (pole strength × separation). Direction: from S to N.
- Torque on a bar magnet in a uniform field: τ = m × B (same as a current loop).
Magnetic Field of a Bar Magnet
- Axial point: B = μ₀(2m)/(4πr³) — same direction as m.
- Equatorial point: B = μ₀(m)/(4πr³) — opposite direction to m.
- 'The field at the axial point is TWICE the field at the equatorial point (at the same distance).'
3. Earth's Magnetism
- The Earth behaves like a giant magnetic dipole with its axis TILTED about 11.5° from the geographic axis.
- Magnetic elements:
- Declination (θ) : Angle between geographic meridian and magnetic meridian.
- Dip or Inclination (δ) : Angle made by the total field with the horizontal.
- Horizontal component (B_H) : B_H = B_E cos δ.
Important Values
- At the magnetic equator: δ = 0°, B_H = maximum.
- At the magnetic poles: δ = 90°, B_H = 0.
- 'A compass needle points to the MAGNETIC north, not the GEOGRAPHIC north. The difference is declination.'
4. Magnetisation and Magnetic Intensity
- Magnetisation (M) : Net magnetic dipole moment per unit volume. 'How aligned are the atomic dipoles?'
- Magnetic intensity (H) : H = B/μ₀ − M. The 'magnetising field.'
- Magnetic susceptibility (χ) : M = χH.
- Relative permeability (μ_r) : μ_r = 1 + χ. B = μ₀μ_r H.
5. Magnetic Materials — Comparison Table
| Property | Diamagnetic | Paramagnetic | Ferromagnetic |
|---|---|---|---|
| χ (susceptibility) | Small and NEGATIVE (−10⁻⁵) | Small and POSITIVE (10⁻⁵ to 10⁻³) | Large and POSITIVE (10³) |
| μ_r | < 1 | > 1 | >> 1 |
| Effect | Weakly REPELLED | Weakly ATTRACTED | Strongly ATTRACTED |
| Examples | Bismuth, Copper, Water | Aluminium, Oxygen | Iron, Nickel, Cobalt |
| Temperature dependence | Independent | χ ∝ 1/T (Curie's law) | Ferro → Para above Curie temp |
| Atomic origin | Induced dipoles OPPOSE field | Permanent atomic dipoles align | Domains of aligned dipoles |
Diamagnetic Material
- 'Diamagnetism is UNIVERSAL — present in ALL materials. But it is WEAK and easily overpowered by para/ferro effects.'
- Example: Water is diamagnetic — a frog can be levitated in a strong magnetic field!
Paramagnetic Material
- 'Atoms have PERMANENT magnetic dipoles that tend to ALIGN with the field, but thermal motion RANDOMISES them.'
Ferromagnetic Material
- 'Ferromagnetic materials have DOMAINS — regions of aligned atomic dipoles. An external field grows the aligned domains at the expense of others.'
- Curie temperature: Above T_C, ferromagnetic becomes paramagnetic. Iron: 770°C.
6. Hysteresis
- The LAG between magnetisation (M) and magnetic intensity (H).
- Hysteresis loop: A closed curve showing M vs H as the field is cycled.
- Retentivity: Remanent magnetisation when H is reduced to zero.
- Coercivity: Reverse H needed to reduce M to zero.
| Type | Retentivity | Coercivity | Use |
|---|---|---|---|
| Soft magnetic | Low | Low | Transformers (easy to magnetise/demagnetise) |
| Hard magnetic | High | High | Permanent magnets |
7. Common Mistakes
- Direction of magnetic moment of a bar magnet: m points from SOUTH to NORTH (inside the magnet). Many students get this backwards.
- Earth's magnetic south is near geographic north: The Earth's magnetic pole near the geographic north pole is actually a SOUTH magnetic pole (attracts the north pole of a compass).
- Paramagnetism vs ferromagnetism: Paramagnetic materials do NOT retain magnetisation when the field is removed. Ferromagnetic materials CAN (permanent magnets).
- Hysteresis loop area: The area of the hysteresis loop represents ENERGY LOST per cycle (as heat).
8. CBSE Exam Focus
- Bar magnet as a dipole — axial and equatorial fields, torque
- Earth's magnetism — magnetic elements (declination, dip, BH)
- Magnetisation and intensity — M, H, χ, μ_r
- Comparison of dia/para/ferro magnetic materials
- Hysteresis — retentivity, coercivity, soft vs hard magnets
- Curie temperature — ferro to para transition
9. Self-Test
Q1: A bar magnet of magnetic moment 2 A·m² is placed in a uniform field of 0.5 T at 30°. Find torque. A1: τ = mB sin θ = 2×0.5×sin30° = 1×0.5 = 0.5 N·m.
Q2: At a certain place, BH = 0.3 G and dip δ = 60°. Find the total field BE. A2: BH = BE cos δ ⇒ BE = BH/cos δ = 0.3/cos60° = 0.3/0.5 = 0.6 G.
Q3: A paramagnetic material has susceptibility 3×10⁻⁴ at 300 K. Find its susceptibility at 600 K. A3: By Curie's law: χ ∝ 1/T. χ₁T₁ = χ₂T₂. (3×10⁻⁴)(300) = χ₂(600) ⇒ χ₂ = (9×10⁻²)/600 = 1.5×10⁻⁴.
Q4: Find the magnetisation M of a solenoid with n=500 turns/m, I=2 A, and core of iron with μr=2000. A4: H = nI = 500×2 = 1000 A/m. B = μ₀μrH = 4π×10⁻⁷×2000×1000 = 2.51 T. M = B/μ₀ − H = (2.51)/(4π×10⁻⁷) − 1000 = 2×10⁶ − 1000 ≈ 2×10⁶ A/m.
Q5: A solenoid of length 10 cm has 500 turns and carries a current of 3 A. Find the magnetic moment. A5: N = 500, I = 3 A, area A = πr² (not given, assume cross-sectional area). Magnetic moment m = NIA = 500×3×A = 1500 A·m² (depends on area). If r is given, substitute.
10. Conclusion
Magnetism in MATTER reveals the quantum nature of materials:
- BAR MAGNET: 'The simplest magnetic object — two poles, a dipole moment, and a field that extends through space.'
- EARTH: 'Our planet is a giant electromagnet — powered by convection in the liquid outer core.'
- MATERIALS: 'Every substance responds to a magnetic field — diamagnets weakly oppose, paramagnets weakly align, ferromagnets STRONGLY align.'
- HYSTERESIS: 'Memory in magnetic materials — the basis of magnetic storage (hard drives, tape).'
'Magnetism is not just a property of magnets — it is a universal property of MATTER itself.'
