Magnetism in matter arises from the orbital and spin magnetic moments of electrons within atoms. All materials respond to magnetic fields, though in very different ways.
Key Concepts
- Bar Magnet: A magnetic dipole with a north and south pole. Magnetic field lines emerge from the north pole and enter the south pole (outside the magnet); inside, they go from south to north. Poles cannot be isolated (magnetic monopoles do not exist).
- Magnetic Dipole Moment (m): m = p × l, where 2l is the length of the magnet and p is the pole strength. Direction: from S to N pole.
- Axial field of a bar magnet: B = µ0 / (4 pi) × 2m / r3 (for short dipole, along the axis)
- Equatorial field: B = µ0 / (4 pi) × m / r3 (along equatorial direction, opposite to m)
- Torque on a dipole: tau = mB sin(theta) = m × B
- Potential energy of dipole: U = -mB cos(theta) = -m · B
- Gauss's Law in magnetism: The total magnetic flux through any closed surface is zero (no magnetic monopoles). Integral(B · dA) = 0.
- Magnetisation (M): Net magnetic dipole moment per unit volume. M = mtotal / V.
- Magnetic Intensity (H): H = B/µ0 - M; unit A/m.
- Magnetic Susceptibility (chim): M = chim × H. Measures how easily a material is magnetised.
- Relative Permeability (µr): µr = 1 + chim; B = µ0 µr H.
- Types of Magnetic Materials:
- Diamagnetic: chim is small and negative (e.g., Bismuth, Copper). Repelled by magnets. They do not have permanent dipoles; opposing magnetisation is induced.
- Paramagnetic: chim is small and positive (e.g., Aluminium, Oxygen). Weakly attracted. Random dipoles align weakly with the field.
- Ferromagnetic: chim is large and positive (e.g., Iron, Nickel, Cobalt). Strongly attracted. Domains align with applied field; retain magnetism.
- Additional Concepts
- Hysteresis: The lag of B behind H in a ferromagnet as the magnetising field changes. The B-H curve forms a closed loop.
- Retentivity: Residual magnetism when H = 0; Coercivity: The reverse H needed to demagnetise.
- Hard and Soft iron: Hard iron has high retentivity and coercivity (permanent magnets); soft iron has low coercivity (electromagnets/transformer cores).
- Curie's Law: For paramagnetics, chim = C/T (C = Curie constant). Susceptibility decreases as temperature rises.
- Curie Temperature: Above the Curie temperature, a ferromagnet becomes paramagnetic.
- Earth's Magnetism: Earth acts as a huge magnet. Geographic north ≠ magnetic north. The angle between the geographic and magnetic meridians is the Magnetic Declination. Magnetic Dip (Inclination) is the angle the resultant Earth field makes with horizontal.
- Key Formulas
- Baxial = µ0 m / (2 pi r3); Bequatorial = µ0 m / (4 pi r3)
- tau = mB sin(theta); U = -mB cos(theta)
- µr = 1 + chim; Curie Law: chim = C/T
---
A bar magnet of moment m = 0.5 A·m2 is placed at angle 30° to a uniform field B = 0.2 T. Find the torque.
tau = mB sin(theta) = 0.5 × 0.2 × sin(30°) = 0.1 × 0.5 = 0.05 N·m
The axial field at 10 cm from a bar magnet is 4 × 10-4 T. Find the magnetic moment.
Baxial = µ0 m / (2 pi r3) = 10-7 × 2m / r3
4 × 10-4 = 2 × 10-7 × m / (10-3) => m = 4 × 10-4 × 10-3 / (2 × 10-7) = 2 A·m2
Classify Bismuth and Iron by their magnetic behaviour and state their susceptibility sign.
Bismuth: diamagnetic — chim is small and negative. Iron: ferromagnetic — chim is large and positive.
At the magnetic equator of Earth, the dip angle is:
At the magnetic equator, the field is horizontal and the dip is 0°.
If a paramagnetic material has chim = 2.6 × 10-5 at 300 K, find chim at 600 K using Curie's law.
chim proportional to 1/T. chim(600) = chim(300) × 300/600 = 2.6 × 10-5 × 0.5 = 1.3 × 10-5
State why the magnetic flux through any closed surface is always zero.
There are no magnetic monopoles. Magnetic field lines always form closed loops (from N to S outside the magnet, and S to N inside). So the net flux entering any closed surface equals the flux leaving it — the total is zero.
A solenoid core material has µr = 500. If H inside is 200 A/m, find B.
B = µ0 µr H = 4 pi × 10-7 × 500 × 200 = 4 pi × 10-7 × 105 = 4 pi × 10-2 ≈ 0.126 T
---
Common mistakes
- Thinking that a magnet's north pole is the actual magnetic north — in fact, Earth's geographic north pole is near the magnetic south pole, so the north pole of a compass (which seeks north) is attracted to it.
- Confusing magnetic dip (the angle of B with horizontal) and declination (horizontal angle from geographic north).
- Hard magnetic materials are used for permanent magnets (high coercivity), NOT soft materials.
Summary
Magnetism in matter is explained through magnetic dipole moments at the atomic level. Materials are classified as diamagnetic, paramagnetic, or ferromagnetic based on their susceptibility. Earth's magnetic field, hysteresis in ferromagnets, and the Curie law are important concepts for CBSE exams.