---
title: "Coercivity and retentivity using BH curve"
subject: "Electrical Machine"
chapter: 1
key: "semester_4/electrical_machine:coercivity-retentivity-bh"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/coercivity-retentivity-bh
site: BCT Engineering
---

# Coercivity and retentivity using BH curve

Electrical Machine · Chapter 1: Magnetic Circuits and Induction

- Asked in: 2073 Magh, 6 marks
- Video: [Electrical Machines | Lecture - 1F | Magnetic Circuits | Magnetic B-H Curve & Hysteresis](https://www.youtube.com/watch?v=6MrybyV0K5c) — Engineering Devotion
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/coercivity-retentivity-bh
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-1

## Question

Define coercivity and retentivity with the help of BH curve.

## Short answer

Retentivity (Br) is the residual flux density when H=0 after saturation; coercivity (Hc) is the reverse field required to demagnetize the material to zero. They are the B-axis and H-axis intercepts of the hysteresis loop.

## Answer

When a ferromagnetic material is magnetised and then demagnetised by an alternating field, the flux density *B* does not retrace its path. The result is a closed **B–H (hysteresis) loop**, and two of its intercepts give the properties asked for.

```text
              B
              |      .------- +Bs
              |    /
          Br -+---/---.
              |  /    |
  ------------+-/-----+-------- H
            -Hc /     +Hc
     -Bs ------'      |
              |
```
Reading the loop: start from the unmagnetised state at the origin and raise H until the material saturates (+Bs). Reducing H to zero leaves the flux density Br. Reversing H to −Hc brings B to zero. Further reversal saturates the material in the opposite direction, and the loop closes in the same way.

#### Retentivity (residual magnetism)
- It is the flux density **Br** that remains in the material when the magnetising field *H* is reduced to zero after the material has been saturated.
- On the loop, it is the intercept on the B-axis.
- High retentivity is needed in permanent magnets. It is also the reason a self-excited dynamo can build up its voltage (from the residual flux of its poles).

#### Coercivity (coercive force)
- It is the reverse magnetising force **Hc** (in A/m) needed to reduce the residual flux density Br to zero.
- On the loop, it is the intercept on the H-axis.
- A large Hc (hard materials such as steel and alnico) is used for permanent magnets. A small Hc (soft iron, silicon steel) is used for the cores of transformers and machines, because the loop is narrow and the hysteresis loss is small.

## Check yourself

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

1. What is retentivity?
   A. The H needed to bring B to zero
   B. The area of the loop
   C. The flux density left when H is reduced to zero after saturation
   D. The maximum flux density in the material
   Answer: C. Retentivity Br is the residual flux density remaining at H = 0, the B-axis intercept. (Key point: Retentivity definition)

2. What is coercivity?
   A. The slope of the B-H curve
   B. The reverse H needed to reduce residual flux density to zero
   C. The flux left at H = 0
   D. The saturation flux density
   Answer: B. Coercive force Hc is the reverse magnetising force that makes B zero, the H-axis intercept. (Key point: Coercivity definition)

3. Which material property suits a permanent magnet?
   A. Narrow loop
   B. Low Hc and low Br
   C. Zero retentivity
   D. Large Hc (hard material such as alnico)
   Answer: D. Permanent magnets need to keep and resist loss of magnetism, so they use hard materials with large Hc and high Br. (Key point: Permanent magnet material)

4. Why do transformer cores use soft iron or silicon steel?
   A. They have infinite resistivity
   B. Small Hc gives a narrow loop and small hysteresis loss
   C. Large Hc gives strong magnets
   D. High retentivity keeps the flux
   Answer: B. A small Hc gives a narrow B-H loop, so loss per cycle is small. (Key point: Core material)

## Related in Electrical Machine

- [Retentivity, coercivity, energy per cycle](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Aretentivity-coercivity-energy-loop) — Electrical Machine, chapter 1
- [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