Magnetic Properties: Types, Domains, Hysteresis, Applications

TAKEAWAYS:

• Materials behave differently in magnetic fields: some repel (diamagnetic), some weakly attract (paramagnetic), and some strongly align (ferromagnetic).
• Magnetic domains are tiny regions where atomic magnets point the same way—how permanent magnets form.
• Hysteresis loops show energy loss in ferromagnetic materials (key for transformers and electromagnets).
• Curie temperature is the point where ferromagnets lose their magnetism (e.g., iron loses it at 770°C).
• Applications range from fridge magnets (ferrites) to MRI machines (superconductors) and credit cards (paramagnetic inks).
• NEB exam focus: Compare properties, sketch hysteresis loops, and explain real-world uses (e.g., why soft iron is used in electromagnets).

1. Magnetic Materials: How They Respond to Fields

All materials have magnetic moments (tiny "compasses" from electron spins). When placed in an external magnetic field $B_{\text{ext}}$, they respond differently:

classDiagram
    class Material {
        <<abstract>>
        +responds_to(B_ext)
    }
    class Diamagnetic {
        +weakly repelled
        +no unpaired electrons
        +example: water, copper
    }
    class Paramagnetic {
        +weakly attracted
        +some unpaired electrons
        +example: aluminum, oxygen
    }
    class Ferromagnetic {
        +strongly attracted
        +permanent domains
        +example: iron, cobalt
    }
    Material <|-- Diamagnetic
    Material <|-- Paramagnetic
    Material <|-- Ferromagnetic

Why the difference?

• Diamagnetic: All electrons are paired → no net magnetic moment. Field induces a tiny opposing moment (Lenz’s law).
• Paramagnetic: Some unpaired electrons → weak attraction (aligns with field but randomizes when field is removed).
• Ferromagnetic: Strong attraction due to domains (groups of aligned atomic magnets).

2. Ferromagnetism: The Strongest Effect

Ferromagnetic materials (Fe, Co, Ni, alloys like Alnico) have:

• Spontaneous magnetization: Domains align even without an external field (why fridge magnets stick!).
• Curie Temperature ($T_C$): Above this, thermal energy randomizes domains. For iron, $T_C=770^{\circ }\text{C}$.

How Domains Work

1. No field: Domains point randomly → net magnetization = 0.
2. Apply field: Domains align with the field → net magnetization increases.
3. Remove field: Some domains stay aligned → permanent magnet.

Example: A paperclip (iron) sticks to a magnet because its domains align with the magnet’s field.

3. Hysteresis Loop: Energy Loss in Ferromagnets

When you magnetize/demagnetize a ferromagnet, its magnetization $M$ lags behind the applied field $B$. This hysteresis loop shows:

Key terms:

• Remanence ($M_r$): Magnetization left when $B_{\text{ext}}=0$ (how "strong" the magnet is).
• Coercivity ($B_c$): Field needed to demagnetize (how "hard" the magnet is).
• Area of loop: Energy lost as heat per cycle (important for transformers!).

Soft vs. Hard Ferromagnets:

4. Other Magnetic Materials

Antiferromagnetism

• Neighboring atoms’ moments cancel out (e.g., MnO).
• No net magnetization → behaves like paramagnets at high temps.

Ferrimagnetism

• Moments partially cancel (e.g., ferrites like ${\text{Fe}}_3{\text{O}}_4$).
• Used in transformers (low eddy current loss).

Superconductors

• Perfect diamagnets below $T_c$ (Meissner effect).
• Expel all magnetic fields → used in MRI machines and maglev trains.

5. Applications in Real Life

6. Solved Example: Hysteresis Loop Calculation

Problem: A ferromagnetic material has remanence $M_r=0.8\text{A/m}$ and coercivity $B_c=200\text{A/m}$. If the loop area represents 50 J/m³ energy loss per cycle, calculate the frequency limit for safe operation in a transformer core (assume $B_{\text{max}}=1\text{T}$).

Solution:

1. Energy loss per cycle ($W$): Given as 50 J/m³.
2. Power loss ($P$): $P=W\times f$, where $f$ is frequency.
   • For safe operation, $P$ must not exceed the core’s heat dissipation (say, 100 W/m³).
   • $100=50\times f$ → $f=2\text{Hz}$.
   • But real transformers use soft iron (low hysteresis loss) to operate at 50–60 Hz!

Key Idea: Hard materials (high $B_c$) lose more energy → limit their use to DC or low-frequency AC.

7. NEB-Style Questions

Short Answer (3 marks)

1. Define coercivity and remanence. Why is soft iron preferred for electromagnet cores?

   • Coercivity: Field needed to demagnetize.
   • Remanence: Magnetization left after removing the field.
   • Soft iron: Low coercivity → less hysteresis loss → more efficient in AC.

2. How does the magnetic behavior of a paramagnetic material differ from a ferromagnetic material?

   • Paramagnetic: Weak attraction, no domains, temporary alignment.
   • Ferromagnetic: Strong attraction, permanent domains, hysteresis.

Long Answer (5 marks)

3. Draw a hysteresis loop for a hard ferromagnetic material and label:

   • Saturation magnetization ($M_s$)
   • Remanence ($M_r$)
   • Coercivity ($B_c$)
   • Explain why hard materials are used in permanent magnets.

4. A student claims, "All ferromagnetic materials are good permanent magnets." Is this true? Justify with examples.

   • False. Soft ferromagnets (e.g., soft iron) have low coercivity → poor permanent magnets but good for electromagnets.
   • Hard ferromagnets (e.g., steel) retain magnetization → good for permanent magnets.

Numerical (4 marks)

5. A toroid has 200 turns and carries 0.5 A. The relative permeability of its core is 500. Calculate:

   • (a) Magnetic field inside the core.
   • (b) If the core is made of soft iron (${\mu }_r=5000$), how does the field change?

   Solution:

   • (a) $B={\mu }_0{\mu }_{r}nI=(4\pi \times 10^{-7})(500)(200)(0.5)=6.28\times 10^{-2}\text{T}$.
   • (b) Higher ${\mu }_r$ → stronger field ($B\propto {\mu }_r$).

Exam Tip

1. Memorize the hierarchy: Diamagnetic < Paramagnetic < Ferromagnetic (in terms of susceptibility $\chi$).
2. Hysteresis loop sketches:
   • Draw soft (narrow loop) vs. hard (wide loop) materials.
   • Label $M_r$, $B_c$, and $M_s$.
3. Applications:
   • Soft iron: Transformers, electromagnets (low $B_c$).
   • Hard steel: Permanent magnets (high $B_c$).
   • Ferrites: Microwaves (non-conductive).
4. Curie temperature: Always mention it’s where ferromagnetism disappears (e.g., iron loses it at 770°C).
5. Units:
   • $B$: Tesla (T) or ${\text{Wb/m}}^2$.
   • $M$: A/m (magnetization).
   • $\chi$: Dimensionless (susceptibility).

Final Note:

• Weak forces (diamagnetic/paramagnetic) are temporary and weak.
• Strong forces (ferromagnetic) involve domains and hysteresis.
• Real-world link: Your phone’s speaker uses ferromagnetic materials, while MRI machines rely on superconductors (perfect diamagnets)!

Practice: Sketch the hysteresis loop for a fridge magnet (hard) vs. a transformer core (soft). Label everything!