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Magnetic Materials

Ch. 11Std 12

Easy Overview

Not all materials respond to magnetic fields in the same way. If you hold a magnet near a piece of iron, it gets attracted. Near aluminium — nothing visible happens, but a very sensitive instrument would detect a weak repulsion. Near wood — absolutely nothing. Why this difference? The answer lies in the atomic structure of materials. Every electron has a magnetic moment due to two sources: (1) its orbital motion around the nucleus (like a tiny current loop) and (2) its intrinsic spin. In most materials, these tiny magnetic moments are randomly oriented and cancel out. But when an external field is applied, they can align to varying degrees, giving rise to different types of magnetism. Diamagnetic materials (copper, bismuth, water) have all electrons paired. When an external field is applied, it induces a weak opposing magnetic moment. They are repelled slightly by magnets. Superconductors are perfect diamagnets (Meissner effect — they expel all magnetic fields and can levitate magnets above them). Paramagnetic materials (aluminium, oxygen, platinum) have unpaired electrons. Their atomic moments align partially with an external field, producing a weak attraction. At higher temperatures, thermal agitation reduces this alignment — magnetism decreases with heating (Curie's law). Ferromagnetic materials (iron, nickel, cobalt) have strong interactions between neighbouring atoms, causing large regions (domains) to align spontaneously. They can retain magnetisation even after the external field is removed — that is how permanent magnets work.

Magnetic Dipole Moment of an Atom

Electron orbital motion: current loop I = e/T = eω/(2π), area A = πr². Magnetic moment m_L = IA = (eωr²)/2. Bohr magneton μ_B = eh/(4πm_e) = 9.27 × 10⁻²⁴ J/T. Electron spin contributes m_S = ±μ_B. Total atomic moment = vector sum of orbital and spin moments.

Magnetisation and Magnetic Intensity

Magnetisation M = magnetic moment per unit volume (A/m). Magnetic intensity H = applied field due to free current (A/m). B = μ₀(H + M). Magnetically: most materials have M ∝ H: M = χ_m H, where χ_m is magnetic susceptibility. B = μ₀(1 + χ_m)H = μ₀μ_r H = μH.

Magnetic Permeability and Susceptibility

Relative permeability μ_r = B/B₀ = 1 + χ_m. Absolute permeability μ = μ₀μ_r. For vacuum: μ_r = 1, χ_m = 0. χ_m > 0 → paramagnetic (μ_r > 1). χ_m < 0 → diamagnetic (μ_r < 1). χ_m >> 0 → ferromagnetic (μ_r >> 1).

Diamagnetism

Present in all materials, but weak. Atoms with all electrons paired (closed shells). Induced magnetic moment opposes applied field (Lenz's law at atomic level). χ_m ≈ −10⁻⁵ to −10⁻⁶. Examples: copper, bismuth, water, gold. Mercury is diamagnetic (levitates in strong field).

Paramagnetism

Atoms with unpaired electrons. Random orientation due to thermal energy. External field aligns moments partially. χ_m ≈ 10⁻³ to 10⁻⁵. Curie's law: χ_m = C/T (C = Curie constant). Langevin theory: M = NμL(y) where L(y) = coth y − 1/y, y = μB/(kT). Examples: Al, Pt, O₂, rare earth ions.

Ferromagnetism

Spontaneous alignment of magnetic moments within domains. Due to quantum exchange interaction. χ_m >> 1 (up to 10⁶). Saturation magnetisation. Curie temperature T_c: ferromagnetic → paramagnetic above T_c. Iron: T_c ≈ 770°C. Hysteresis: B does not follow H reversibly.

Domain Theory of Ferromagnetism

Ferromagnetic materials consist of domains (~1 mm to 1 µm). Each domain is fully magnetised but domains point in different directions. Net magnetisation ~ 0 without field. Applied field: domain walls move (favourable domains grow). Strong field: domain rotation. Saturation: all domains aligned.

Hysteresis Loop (B-H Curve)

Starting from unmagnetised: H ↑ → B ↑ to saturation. H ↓ → B does not return along same path. B at H = 0 is remanence B_r. Reverse H to make B = 0: coercivity H_c. Full loop: area = energy loss per cycle (hysteresis loss).

Hard and Soft Magnetic Materials

Soft iron: narrow hysteresis loop, low H_c (easy to magnetise/demagnetise). Used in transformers, electromagnets — low hysteresis loss. Steel (hard): wide loop, high H_c, high B_r. Used for permanent magnets. Alnico, ferrites, NdFeB magnets.

Curie's Law and Curie Temperature

Curie law for paramagnets: χ_m = C/T. Curie-Weiss law for ferromagnets above T_c: χ_m = C/(T − T_c). Below T_c, spontaneous magnetisation exists. At T_c, thermal energy overcomes exchange interaction. For iron: T_c = 1043 K. Heating a permanent magnet above T_c destroys its magnetism.

Electromagnets and Permanent Magnets

Electromagnet: soft iron core inside solenoid. High B, negligible remanence — magnetic only when current flows. Earth magnets: used in MRI (2 T), particle accelerators (8 T). Permanent magnets: hard ferromagnetic materials with high B_r and H_c. Applications: speakers, motors, generators, magnetic separators.

Magnetic Properties of Superconductors

Type I superconductors: perfect diamagnets below T_c — Meissner effect: B = 0 inside. χ_m = −1. Magnetic levitation. Type II: allow partial field penetration (vortices) above H_c1. High-T_c superconductors are type II. Applications: maglev trains, MRI.

Magnetic Shielding

High permeability materials (mu-metal) redirect magnetic field lines. Used to shield sensitive equipment from magnetic interference (CRT monitors, electron microscopes, biomedical sensors). Earth's field must be shielded for precise magnetic measurements.

Key Points

  • •Bohr magneton μ_B = eh/(4πm_e) = 9.27 × 10⁻²⁴ J/T.
  • •Magnetisation M = magnetic moment/volume. B = μ₀(H + M).
  • •Magnetic susceptibility χ_m = M/H. μ_r = 1 + χ_m.
  • •Diamagnetic: χ_m < 0 (all electrons paired). μ_r < 1.
  • •Paramagnetic: χ_m > 0 (unpaired electrons). Curie law.
  • •Ferromagnetic: χ_m >> 1. Domains. Curie temperature.
  • •Hysteresis: B_r (remanence), H_c (coercivity).
  • •Soft: narrow loop, low loss. Hard: wide loop, permanent magnet.
  • •Superconductors: perfect diamagnets (Meissner effect, χ_m = −1).

Practice Questions

  • Distinguish between diamagnetic, paramagnetic, and ferromagnetic materials with examples. Give properties of each.
  • What is hysteresis? Draw and explain B-H curve for a ferromagnetic material. Define retentivity and coercivity.
  • Explain domain theory of ferromagnetism. How do domains behave when an external magnetic field is applied?
  • State Curie's law for paramagnetic materials. What is Curie temperature? What happens to a ferromagnet above its Curie temperature?
  • Distinguish between hard and soft magnetic materials. Give two applications of each.
  • What is magnetic susceptibility? Define relative permeability. Derive relation: μ_r = 1 + χ_m.
  • Explain the magnetic properties of superconductors. What is the Meissner effect?
  • An iron rod of cross-section 2 cm² and μ_r = 1000 is placed in a solenoid. Current 1 A, length 50 cm, 2000 turns. Find B, M, H.