---
title: "Significance of hysteresis loop, volume dependence"
subject: "Electrical Machines"
chapter: 1
key: "semester_4/electrical_machines:hysteresis-loop-significance"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/hysteresis-loop-significance
site: BCT Engineering
---

# Significance of hysteresis loop, volume dependence

Electrical Machines · Chapter 1: Magnetic Circuits and Induction

- Asked in: 2079 Jestha, 2+6 marks
- Video: [What is Hysteresis Loop? | Hysteresis Loss Explained in Hindi | B-H Curve, Retentivity, Coercivity](https://www.youtube.com/watch?v=VCoDHTIWUaA) — Electrical Engineering MCQ's
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/hysteresis-loop-significance
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-1

## Question

Explain the significance of hysteresis loop for ferromagnetic materials used in electrical machine. Justify that hysteresis power loss is dependent on the volume of core material.

## Short answer

The loop shows retentivity, coercivity, saturation flux density and area. Area equals energy lost per cycle per unit volume; loss per cycle scales with volume, so P_h = η B_max^x f V, directly proportional to volume.

## Answer

The hysteresis loop is the closed $B$–$H$ curve traced by a ferromagnetic material when $H$ is taken through a full cycle. It shows how the flux density lags behind the magnetising force, and its shape and area decide where a material can be used.

#### Significance of the hysteresis loop

```text
      B
      |      ___---- Bs (saturation)
      |   .-'
   Br |--/---.
      | /     \
 -----+-+------+------ H
   -Hc|        Hc
      |
```

1. **Retentivity ($B_r$):** the flux density left when $H = 0$. A high $B_r$ is needed for permanent magnets.
2. **Coercivity ($H_c$):** the reverse field needed to bring $B$ to zero. A small $H_c$ gives a narrow loop (soft iron, silicon steel) for transformer and armature cores. A large $H_c$ gives a wide loop (hard steel, alnico) for permanent magnets.
3. **Area of the loop:** it equals the energy lost as heat per cycle per unit volume. A narrow loop means low hysteresis loss and high efficiency.
4. **Saturation flux density ($B_s$):** it fixes the highest flux a core can carry, so it limits the size of the machine.
5. **Material selection:** the loop shows at a glance whether the material suits an ac machine core (narrow loop) or a permanent magnet (wide loop).

#### Hysteresis loss depends on volume

Energy spent in one cycle per unit volume is the loop area:

$$
w_h = \oint H\,dB\ \ \text{J/m}^3\text{ per cycle}
$$

This value depends only on the material and on $B_{max}$, not on the size of the core. A core of volume $V$ has $V$ times as much material taking part in the magnetisation reversal, so

$$
\begin{aligned}
\text{Energy per cycle} &= w_h V \\
P_h &= w_h V f = \eta B_{max}^{x} f V\ \ \text{W}
\end{aligned}
$$

where $\eta$ is the Steinmetz coefficient and $x \approx 1.6$ to $2$. Hence $P_h \propto V$: doubling the core volume at the same $B_{max}$ and $f$ doubles the hysteresis loss. This is why machine cores are made as small as the design allows.

## Check yourself

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

1. What does the area of the B-H loop represent?
   A. Energy lost as heat per cycle per unit volume
   B. Total flux in the core
   C. The saturation flux density
   D. Permeability of the material
   Answer: A. The loop area equals the hysteresis energy loss per cycle per unit volume. (Key point: Loop area meaning)

2. Which loop suits a transformer core, and which suits a permanent magnet?
   A. Wide for transformer, narrow for magnet
   B. Narrow for both
   C. Narrow for transformer, wide for magnet
   D. Wide for both
   Answer: C. A narrow loop (small H_c) gives low loss for ac cores; a wide loop (large H_c, high B_r) suits permanent magnets. (Key point: Soft vs hard material)

3. Why is hysteresis loss proportional to core volume?
   A. Energy per cycle per unit volume is fixed by material and B_max, so more material means proportionally more loss
   B. Loop area increases with the core size
   C. Larger cores run at higher frequency
   D. Larger cores have a larger Steinmetz exponent
   Answer: A. w_h depends only on material and B_max, so P_h = w_h V f scales with V. (Key point: Loss proportional to volume)

4. What is retentivity B_r?
   A. The reverse H needed to make B zero
   B. The flux density remaining when H returns to zero
   C. The maximum flux density of the material
   D. The slope of the B-H curve
   Answer: B. B_r is the residual flux density left at H = 0; the reverse field to cancel it is the coercivity. (Key point: Retentivity)

## Related in Electrical Machines

- [Hysteresis loop area and energy loss](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ahysteresis-loop-area-energy-loss) — Electrical Machines I, 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
- [No-load current components, iron loss and core flux](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ano-load-current-10a-0p3pf-500turns) — Electrical Machines I, chapter 2
- [Why rotor core loss is negligible](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Arotor-core-loss-negligible) — Electrical Machines, chapter 5, asked 2×
- [Retentivity, coercivity and hysteresis energy](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aretentivity-coercivity-hysteresis-energy) — Electrical Machines I, chapter 1
- [Magnetic hysteresis and energy per cycle](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Ahysteresis-energy-loop-area) — Electrical Machines, chapter 1

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