Magnetism and Matter
1. Introduction
This chapter explores the nature of magnetism, magnetic materials, and the Earth's magnetic field — connecting microscopic magnetic properties to macroscopic observations.
2. Bar Magnet
A bar magnet has two poles: north and south. Magnetic field lines emerge from north and enter south (outside the magnet).
2.1 Magnetic Moment
m = pole strength × magnetic length. Direction from south to north.
2.2 Field Due to a Bar Magnet
At axial point: B = μ₀/4π × 2M/r³ At equatorial point: B = μ₀/4π × M/r³
2.3 Torque in Uniform Field
τ = m × B, magnitude = mB sin θ.
3. Earth's Magnetism
The Earth behaves like a giant bar magnet with its magnetic south pole near the geographic north pole.
Elements of Earth's magnetism:
- Declination: Angle between magnetic meridian and geographic meridian.
- Inclination (dip): Angle of the Earth's total magnetic field with the horizontal. At the magnetic equator, dip = 0°. At magnetic poles, dip = 90°.
- Horizontal component: B_H = B_E cos δ.
4. Magnetic Materials
4.1 Diamagnetic Materials
- Weakly repelled by magnets.
- μᵣ < 1, χ_m is small and negative.
- Examples: Bismuth, Copper, Water, Gold.
- Susceptibility is independent of temperature.
4.2 Paramagnetic Materials
- Weakly attracted by magnets.
- μᵣ > 1, χ_m is small and positive.
- Examples: Aluminum, Platinum, Oxygen, Manganese.
- χ_m ∝ 1/T (Curie's law).
4.3 Ferromagnetic Materials
- Strongly attracted by magnets.
- μᵣ >> 1, χ_m is large and positive.
- Examples: Iron, Nickel, Cobalt, Steel.
- Show hysteresis and have a Curie temperature above which they become paramagnetic.
4.4 Comparison of Magnetic Materials
| Property | Diamagnetic | Paramagnetic | Ferromagnetic |
|---|---|---|---|
| Susceptibility (χ_m) | Negative, small | Positive, small | Positive, large |
| Relative permeability (μᵣ) | < 1 | > 1 | >> 1 |
| Effect of magnet | Weakly repelled | Weakly attracted | Strongly attracted |
| Temperature dependence | Independent | χ ∝ 1/T (Curie's law) | Ferro → Para above Curie temp |
| Examples | Bi, Cu, H₂O | Al, Pt, O₂ | Fe, Ni, Co |
| Atomic/electronic basis | All electrons paired | Unpaired electrons | Domain alignment |
5. Hysteresis
The lag between magnetization and the applied magnetic field. The hysteresis loop shows:
- Retentivity (residual magnetization when H = 0).
- Coercivity (reverse H needed to reduce B to zero).
6. Permanent Magnets
Materials with high retentivity and high coercivity (hard ferromagnetic materials). Used in speakers, generators, and magnetic sensors.
7. Worked Problems
Problem 1: The Earth's horizontal component is 0.3 G and dip angle is 60°. Find the total Earth's magnetic field. Solution: B_E = B_H/cos δ = 0.3/cos 60° = 0.3/0.5 = 0.6 G.
Problem 2: A bar magnet of magnetic moment 5 Am² is placed at 30° to a uniform field of 0.2 T. Find torque. Solution: τ = mB sin θ = 5 × 0.2 × sin 30° = 1 × 0.5 = 0.5 Nm.
Problem 3: Compare the properties of diamagnetic, paramagnetic, and ferromagnetic materials. Solution: Table comparison with susceptibility, permeability, temperature dependence, and examples.
8. Common Mistakes
'Students often think the north pole of a compass points to the Earth's magnetic north pole. Actually, it points to the Earth's magnetic south pole (which is near the geographic north pole).'
9. ISC Exam Focus
| Topic | Theory Marks | Practical Marks |
|---|---|---|
| Bar magnet | 3 | 1 |
| Earth's magnetism | 3 | 2 |
| Magnetic materials | 4 | 2 |
| Hysteresis | 2 | 1 |
10. Self-Test Questions
- Derive the expression for magnetic field due to a bar magnet at an axial point.
- Define angle of dip and angle of declination. How are they related to the Earth's magnetic field?
- Distinguish between diamagnetic, paramagnetic, and ferromagnetic materials on the basis of susceptibility and permeability.
- Explain hysteresis and what is meant by retentivity and coercivity.
- Find the magnetic moment of a bar magnet placed at 45° to a uniform field of 0.1 T experiencing a torque of 0.02 Nm.
11. Comparison of Magnetic Materials
| Property | Diamagnetic | Paramagnetic | Ferromagnetic |
|---|---|---|---|
| Magnetic susceptibility (χₘ) | Negative, small | Positive, small | Positive, large |
| Relative permeability (μᵣ) | < 1 | > 1 | >> 1 |
| Effect of external field | Weakly repelled | Weakly attracted | Strongly attracted |
| Temperature dependence | Independent | χ ∝ 1/T (Curie's law) | Curie temperature → paramagnetic |
| Examples | Bi, Cu, Au, H₂O | Al, Pt, O₂, Mn | Fe, Ni, Co, Steel |
12. Additional Worked Problems
Problem A: The horizontal component of Earth's magnetic field at a place is 0.28 G and the angle of dip is 30°. Find the vertical component and the total field.
Solution: B_V = B_H tan δ = 0.28 × tan 30° = 0.28 × 0.577 = 0.162 G. B_E = B_H/cos δ = 0.28/cos 30° = 0.28/0.866 = 0.323 G.
Problem B: A bar magnet of magnetic moment 2 Am² has a pole strength of 10 Am. Find its magnetic length.
Solution: m = pole strength × magnetic length ⇒ 2 = 10 × 2ℓ ⇒ ℓ = 0.1 m = 10 cm. The actual length of the magnet is approximately 2ℓ = 20 cm.
Problem C: Explain why ferromagnetic materials are used for making permanent magnets while paramagnetic materials are not.
Solution: Ferromagnetic materials have high retentivity (retain magnetization) and high coercivity (resist demagnetization). Paramagnetic materials have very low retentivity and lose magnetization as soon as the external field is removed. Permanent magnets require high retentivity and coercivity, which only hard ferromagnetic materials possess.
