Magnetism and Matter
What is examined
Magnetism and Matter covers the bar magnet as a magnetic dipole, field on axial and equatorial lines, Gauss's law for magnetism, earth's magnetism, magnetic properties of materials, hysteresis and the choice of magnetic materials.
Core rules
- Magnetic moment m = NIA, direction from S to N inside the magnet.
- Axial field: B = (μ₀/4π)(2m/r³). Equatorial field: B = (μ₀/4π)(m/r³), opposite to m.
- Gauss's law for magnetism: ∮B·dS = 0 - no magnetic monopoles; field lines are closed loops.
- Earth's magnetism: declination D, dip (inclination) δ, horizontal component H. Then B = H/cos δ and vertical component V = H tan δ.
- Magnetisation M = m/V; susceptibility χ = M/H; permeability μ = μ₀(1 + χ).
- Dia-, para- and ferromagnets differ in χ (small negative, small positive, very large) and in temperature behaviour; Curie law χ ∝ 1/T for paramagnets; ferromagnets lose order above the Curie temperature.
- Hysteresis: soft iron has a narrow loop (electromagnet cores, transformers); steel has a wide loop and high retentivity (permanent magnets).
Worked example
At a place H = 0.30 G and dip δ = 30°. Find B and V. B = H/cos 30° = 0.30/0.866 ≈ 0.35 G. V = H tan 30° = 0.30 × 0.577 ≈ 0.17 G. Reasoning: B is the total earth's field; H is its horizontal part; δ is the angle B makes with the horizontal.
Traps
Swapping the axial factor 2; using r² instead of r³; mixing up dip and declination; and choosing steel for a transformer core or soft iron for a permanent magnet.