---
title: "Domains, domain walls and magnetic losses"
subject: "Electrical Engineering Material"
chapter: 4
key: "semester_3/electrical_engineering_material:domain-walls-magnetic-losses"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/domain-walls-magnetic-losses
site: BCT Engineering
---

# Domains, domain walls and magnetic losses

Electrical Engineering Material · Chapter 4: Magnetic Materials

- Asked in: 2076 Asoj, 2+4+2 marks
- Video: [Magnetic Domains {Texas A&M: Intro to Materials (MSEN 201)}](https://www.youtube.com/watch?v=koeDE-O18I8) — Patrick Shamberger
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/domain-walls-magnetic-losses
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-4

## Question

Define magnetic domain and domain walls in magnetic materials. Explain in brief about losses that would occur in magnetic materials.

## Short answer

A magnetic domain is a region where all atomic moments align in one direction to saturation. A domain wall is a thin boundary where spin orientation rotates gradually between domains. Core losses include hysteresis loss (energy/cycle = B-H loop area), eddy-current loss (by induced currents, reduced by laminations), and anomalous loss due to Barkhausen jumps.

## Answer

#### Magnetic domain
A **magnetic domain** is a small region (about $10^{-6}$–$10^{-3}$ m) inside a ferromagnetic material in which all atomic magnetic moments are aligned in the same direction by the exchange interaction, so the region is magnetized to saturation.

#### Domain wall
A **domain wall** (Bloch wall) is the transition layer, a few hundred atoms thick, separating two adjacent domains. Across it the direction of the moments rotates gradually from that of one domain to the other.

```text
 domain 1  | wall          | domain 2
 ^ ^ ^ ^   | ^ / -> \ v    | v v v v
```

#### Losses in magnetic materials
When a magnetic core carries alternating flux, part of the input energy is turned into heat. These **core (iron) losses** are:

1. **Hysteresis loss**
   - Energy spent in moving domain walls and rotating domains back and forth each cycle; equals the area of the B–H loop per cycle per m³.
   - Steinmetz formula: $P_h = \eta\,B_{max}^{1.6}\,f\,V$
   - Reduced by soft materials with a narrow loop (silicon steel, CRGO).

2. **Eddy-current loss**
   - Alternating flux induces emfs and circulating currents in the conducting core, causing $I^2R$ heating.
   - $P_e = K_e\,B_{max}^2\,f^2\,t^2\,V$ (t = lamination thickness)
   - Reduced by thin insulated laminations, adding silicon to raise resistivity, or using ferrites/powder cores.

3. **Anomalous (excess/residual) loss**
   - Extra eddy loss from local, jerky domain wall motion (Barkhausen jumps); becomes important at high frequency.

Total core loss $P_c = P_h + P_e (+ P_{anom})$; it appears as heat and lowers efficiency of transformers and machines.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is a domain wall?
   A. A transition layer a few hundred atoms thick in which moments rotate gradually from one domain direction to the next
   B. A sharp boundary where moments reverse abruptly in one atom
   C. A crack in the crystal
   D. A region with zero moments
   Answer: A. Across a Bloch wall the moment direction turns gradually. (Key point: Domain wall)

2. What does hysteresis loss per cycle per m^3 equal?
   A. The height of the loop only
   B. The area of the B-H loop
   C. The coercivity squared
   D. The saturation flux density
   Answer: B. Energy spent moving walls and rotating domains each cycle equals the loop area. (Key point: Hysteresis loss)

3. How is eddy-current loss reduced in a core?
   A. Using thicker laminations
   B. Lowering the resistivity
   C. Thin insulated laminations, silicon addition to raise resistivity, or ferrites
   D. Raising the frequency
   Answer: C. Pe is proportional to t^2 and f^2, and inversely depends on resistivity, so thin laminations and high resistivity help. (Key point: Eddy-current loss)

4. How do hysteresis and eddy-current losses vary with frequency?
   A. Both proportional to f^2
   B. Hysteresis proportional to f^2; eddy to f
   C. Both independent of f
   D. Hysteresis loss is proportional to f; eddy loss is proportional to f^2
   Answer: D. Ph = η Bmax^1.6 f V and Pe = Ke Bmax^2 f^2 t^2 V. (Key point: Frequency dependence)

## Related in Electrical Engineering Material

- [Domain walls and demagnetization process](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Adomain-walls-demagnetization) — Electrical Engineering Material, chapter 4
- [Magnetic domains in an external field](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Adomains-in-external-field) — Electrical Engineering Material, chapter 4, asked 3×
- [Hard vs soft magnetic materials for relays](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Ahard-soft-relay) — Electrical Engineering Material, chapter 4
- [Closure domains and demagnetization](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aclosure-domains-demagnetization) — Electrical Engineering Material, chapter 4
- [Applications of soft magnetic materials](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Asoft-magnetic-applications) — Electrical Engineering Material, chapter 4, asked 2×
- [Properties and uses of soft magnetic materials](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Asoft-magnetic-properties-uses) — Electrical Engineering Material, chapter 4

## Related in other subjects

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- [Soft versus hard magnetic materials](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Asoft-hard-magnetic-materials) — Electric Machine Design, chapter 1, asked 5×
- [Soft magnetic materials and commercial applications](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Asoft-magnetic-applications) — Electric Machine Design, chapter 1, asked 2×
- [Hysteresis loop energy, hard and soft magnetic materials](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ahysteresis-area-energy-hard-soft) — Electrical Machines I, chapter 1