Magnetic Materials

Magnetic Materials

1. Magnetization — $B, H, M$

In matter, total field

where $H$ = magnetic field intensity (due to free currents, A/m), $M$ = magnetization (magnetic moment per volume due to bound currents).

For linear isotropic material:

where $χ_m$ = magnetic susceptibility, $μ_r =1+χ_m$ = relative permeability, $μ = μ_0 μ_r$.

2. Classification (exam table — memorize)

Type	$χ_m$	$μ_r$	Behaviour	Example	Origin
Diamagnetic	small negative $∼-10^{-5}$	<1 (≈0.9999)	Weakly repelled, $M$ opposite $B$; no permanent moment; $χ$ ∼$-10^{-5}$ independent of $T$	Cu, Bi, Si, water, superconductor $χ=-1$ (perfect)	Orbital motion (Lenz)
Paramagnetic	small positive $∼10^{-3}$–$10^{-5}$	>1 (≈1.001)	Weakly attracted, $M$ ∥ $B$; random thermal disrupts; Curie law $χ=C/T$	Al, O₂, Mn	Unpaired spins align weakly
Ferromagnetic	large positive $10^{3}$–$10^{5}$	≫1	Strongly attracted, hysteresis, domains, Curie temp above which becomes paramagnetic ($χ=C/(T-T_C)$)	Fe, Ni, Co, ferrites	Domains, exchange

• Ferrimagnetic (ferrite) and antiferromagnetic are ordered variants but syllabus often just mentions ferromagnetic.

3. Hysteresis (ferromagnets)

$B$ vs $H$ loop: saturation $B_s$, remanence $B_r$ (retained at $H=0$), coercivity $H_c$ (field to demagnetize), area = energy loss per cycle. Hard magnets large $H_c$ (permanent), soft small $H_c$ (transformer core).

4. Worked Checks

(a) Iron μ_r≈5000 ⇒ B=μ0·5000·H ⇒ for H=100 A/m, B≈0.628 T (vs vacuum 0.000126 T) ✓

(b) Why superconductor perfect diamagnet? χ=-1 ⇒ B=0 inside (Meissner).

(c) Susceptibility sign tells type.

5. Exam Points

• Define $B=μ0(H+M)$, $χ_m, μ_r$ — 5 marks, very frequent.
• Classify diamagnetic/paramagnetic/ferromagnetic with $χ$ sign/magnitude, example — 5-7 marks, very frequent (table).
• Hysteresis loop with $B_r, H_c$ — 5 marks, frequent.
• Curie law — 3 marks.