PhysicsISC Class 12 · Magnetism and Matter

Hysteresis, Retentivity and Coercivity: Electromagnets and Permanent Magnets

Updated 15 October 2026 · Fact-checked

In a ferromagnet taken through a magnetising cycle, B lags behind H, tracing a closed B-H (hysteresis) loop. Retentivity is the B left when H returns to zero; coercivity is the reverse H needed to bring B to zero. Permanent magnets need high retentivity and coercivity (steel); electromagnet and transformer cores need high permeability and low coercivity (soft iron).

Understand Hysteresis and Permanent Magnets

Magnetising a ferromagnet. Place an unmagnetised ferromagnetic rod in a solenoid and slowly increase H = nI. B rises steeply at first (domains grow and rotate) and then levels off at saturation, when nearly all domains point along H.

The hysteresis loop (qualitative). Now reduce H to zero. B does not retrace the curve: it stays behind. At H = 0 a field remains:

Retentivity (remanence) $B_{r}$ : the value of B left in the material when H is reduced to zero after saturation. It measures how strongly the material keeps its magnetism.

Reverse the current, so H is negative. B falls and reaches zero at:

Coercivity (coercive force) $H_{c}$ : the magnitude of the reverse H needed to bring B to zero. It measures how hard the material is to demagnetise.

Increasing the reverse H saturates the sample the other way; bringing H back to zero and then positive again completes a closed loop. The lagging of B behind H is hysteresis (from a Greek word meaning "to lag").

Energy loss. Over each complete cycle, energy is used in turning domains back and forth and appears as heat. The energy lost per unit volume per cycle equals the area of the B-H loop. A wide loop wastes much energy in alternating fields; a narrow loop wastes little.

Soft and hard magnetic materials.

Property	Soft iron	Steel (and alloys like alnico)
Loop	narrow, tall	wide
Permeability	high	lower
Retentivity	lower (but still noticeable)	high
Coercivity	very low	high
Hysteresis loss	small	large

Choosing materials.

Permanent magnets must keep their magnetism and resist being demagnetised by stray fields, knocks or heating: high retentivity and high coercivity. Steel, alnico and similar alloys.
Electromagnets must become strongly magnetised with a small current and lose the magnetism as soon as the current is switched off: high permeability, low retentivity and low coercivity. Soft iron.
Transformer cores, taken round the loop 50 times a second, must waste little energy: narrow loop (low hysteresis loss), high permeability, low coercivity. Soft iron (laminated, to reduce eddy currents).

Electromagnets. A coil wound on a soft iron core. Inside, $B = μ_{0} μ_{r} n I$ until the core approaches saturation. The strength depends on:
1. the current I;
2. the number of turns per unit length n;
3. the relative permeability of the core (and its shape: a U-shaped core with a short air gap works best).
Uses: cranes, electric bells, relays, loudspeakers, MRI magnets. Once the core saturates, extra current gives little extra B.

Permanent magnets. Made by placing a hard material in a strong field (from a solenoid carrying a large d.c. current) and then removing it; the high retentivity keeps it magnetised. Heating above the Curie temperature, strong reverse fields or repeated knocks can demagnetise it, which is why high coercivity matters.

Hysteresis and Permanent Magnets: formulas and key facts

Field in an electromagnet: $B = μ_{0} μ_{r} n I$; Until the core saturates.
Magnetic intensity: $H = n I$; Set by the coil current.
Retentivity: $B_{r} = B at H = 0$; After saturation.
Coercivity: $H_{c} = ∣ H ∣ at B = 0$; Reverse intensity needed.
Hysteresis loss: $\frac{energy}{volume \times cycle} = loop area$; Power loss = area × volume × frequency.

How to solve Hysteresis and Permanent Magnets questions

Hysteresis questions are mostly explanations; the numericals involve electromagnet fields or the energy lost per cycle.

1For a loop sketch, label axes B and H, saturation, retentivity ( $B_{r}$ on the B-axis) and coercivity ( $H_{c}$ on the negative H-axis).
2For material choice, ask: must it keep its magnetism (high $B_{r}$ , high $H_{c}$ ) or lose it quickly and waste little energy (low $H_{c}$ , narrow loop, high μ)?
3For an electromagnet, find H = nI, then $B = μ_{0} μ_{r} H$ .
4For energy loss, multiply loop area (J m⁻³ per cycle) by volume and frequency.
5Mention saturation when asked why B stops increasing.

Hysteresis and Permanent Magnets in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

An electromagnet in a door bell

Suppose a door bell's electromagnet has 3000 turns per metre, carries 0.1 A and has a soft iron core of relative permeability 400.

Find the field in the core. Why is soft iron, not steel, used?

Try it first, then show the solutionSolution

$B = μ_{0} μ_{r} n I = 4 π \times 1 0^{- 7} \times 400 \times 3000 \times 0.1 \approx 0.15$ T.
When the button is released the core must lose its magnetism at once so the hammer springs back: soft iron has low retentivity and coercivity.

Answer: About 0.15 T; soft iron magnetises easily and loses its magnetism when the current stops.

Memory hook: Electromagnet: easy on, easy off.

High coercivity for data storage

Imagine the magnetic stripe on a library card, which stores data as tiny magnetised regions.

Should the stripe material have high or low coercivity? Explain.

Try it first, then show the solutionSolution

Stray fields from phones, handbags or other cards act like small reverse values of H.
A high-coercivity material needs a large reverse H to demagnetise it, so the stored pattern survives.

Answer: High coercivity (and good retentivity), so that everyday fields cannot erase the data.

Memory hook: Keep it: high $B_{r}$ , high $H_{c}$ .

Tricks to remember Hysteresis and Permanent Magnets

Short memory aids. Say each one aloud once, then use it on a question the same day.

R on B, C on H
Retentivity is read on the B-axis; Coercivity on the H-axis.
Use it when: Labelling the loop.
Soft = easy come, easy go
Soft iron: magnetised easily, demagnetised easily, little loss.
Use it when: Electromagnets and transformer cores.
Hard = hard to lose
Steel: high coercivity, high retentivity.
Use it when: Permanent magnets.
Area = heat
Loop area is the energy wasted per unit volume per cycle.
Use it when: Hysteresis loss.

Hysteresis and Permanent Magnets: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Meaning of coercivity · 1 mark · MCQBoard level

The coercivity of a ferromagnetic material is:
(a) the value of B when H is zero
(b) the reverse H needed to reduce B to zero after saturation
(c) the maximum value of B
(d) the area of the B-H loop

Try it first, then show the solutionSolution

Coercivity is read on the (negative) H-axis where the loop crosses it.

Answer: (b).

Example 2: Labelling a hysteresis loop · 2 marks · Short answerBoard level

Sketch the B-H loop of a ferromagnetic material and mark retentivity and coercivity on it. Define each.

Try it first, then show the solutionSolution

Sketch: closed loop symmetric about the origin, with saturation at the ends; retentivity $B_{r}$ where the loop cuts the +B axis; coercivity $H_{c}$ where it cuts the −H axis. (1)
Retentivity: B remaining when H is reduced to zero after saturation. Coercivity: reverse H needed to make B zero. (1)

Answer: As described: $B_{r}$ on the B-axis, $H_{c}$ on the H-axis.

Example 3: Choosing materials · 3 marks · Long answerHarder board level

State, with reasons, the magnetic properties needed for the material of (a) a permanent magnet, (b) an electromagnet core, (c) a transformer core. Name a suitable material for each.

Try it first, then show the solutionSolution

(a) High retentivity and high coercivity, so it stays magnetised and resists demagnetisation: steel or alnico. (1)
(b) High permeability with low retentivity and coercivity, so a small current gives a strong field that vanishes when switched off: soft iron. (1)
(c) Narrow loop (small hysteresis loss per cycle), high permeability and low coercivity, because it is cycled rapidly: soft iron, laminated. (1)

Answer: Steel/alnico; soft iron; laminated soft iron.

Example 4: Field of an electromagnet · 2 marks · Short answerHarder board level

An electromagnet has 1500 turns per metre and carries 0.8 A; its core has relative permeability 800 (not saturated). Find B in the core. What happens to B if the current is halved?

Try it first, then show the solutionSolution

$B = μ_{0} μ_{r} n I = 4 π \times 1 0^{- 7} \times 800 \times 1500 \times 0.8 \approx 1.21$ T. (1)
B ∝ I below saturation, so it halves to about 0.60 T. (1)

Answer: About 1.21 T; about 0.60 T.

Example 5: Hysteresis loss in a core · 3 marks · Short answerHOTS / competency

The B-H loop of a core material encloses an area equivalent to 300 J m⁻³ per cycle; a better material has a loop area of 30 J m⁻³ per cycle. Find the power wasted in a core of volume $1 \times 1 0^{- 3}$ m³ at 50 Hz for each, and say which is better for a transformer.

Try it first, then show the solutionSolution

Energy per cycle = area × volume: $300 \times 1 0^{- 3} = 0.3$ J and $30 \times 1 0^{- 3} = 0.03$ J. (1)
Power = energy per cycle × cycles per second: $0.3 \times 50 = 15$ W and $0.03 \times 50 = 1.5$ W. (1)
The narrow-loop material wastes ten times less: better for a transformer. (1)

Answer: 15 W and 1.5 W; the narrow-loop material.

Example 6: Designing a lifting magnet · 4 marks · Case-basedHOTS / competency

Suppose a scrapyard lifting magnet must produce B = 1.0 T in its core, which has 500 turns per metre.
(i) Find the current needed with a core of relative permeability 1000. (1 mark)
(ii) Find the current needed with no core. (1 mark)
(iii) Why must the core be soft iron and not steel? (1 mark)
(iv) How could the same field be obtained with half the current? (1 mark)

Try it first, then show the solutionSolution

(i) $I = \frac{B}{μ _{0} μ _{r} n} = \frac{1.0}{4 π \times 1 0 ^{- 7} \times 1000 \times 500} \approx 1.6$ A.
(ii) Without a core, $I = \frac{1.0}{4 π \times 1 0 ^{- 7} \times 500} \approx 1.6 \times 1 0^{3}$ A: impractical.
(iii) The load must drop when the current is switched off: soft iron has low retentivity and coercivity; steel would hold the scrap.
(iv) Double the turns per metre (or use a core of twice the permeability, if not saturated).

Answer: (i) ≈ 1.6 A; (ii) ≈ 1600 A; (iii) low retentivity and coercivity; (iv) double n.

Where students lose marks in Hysteresis and Permanent Magnets

The slips examiners see most often, and what to write instead.

Mistake: Retentivity and coercivity swapped
Students mark coercivity on the B-axis.
Wrong working
Coercivity = B at H = 0.
Right working
Coercivity = |H| at B = 0.
Do this: R on the B-axis, C on the H-axis.
Usually costs: 1 mark.
Mistake: Choosing steel for a transformer
A wide loop means large energy loss every cycle.
Do this: Transformers need narrow loops: soft iron.
Usually costs: 1 mark.
Mistake: Calling soft iron "non-magnetic"
Soft iron is strongly ferromagnetic; it just loses magnetism easily.
Do this: Say "high permeability, low retentivity and coercivity".
Usually costs: ½ to 1 mark.
Mistake: Ignoring saturation
Assuming B keeps rising in proportion to I for an iron core.
Do this: Note that $B = μ_{0} μ_{r} n I$ holds only below saturation.
Usually costs: 1 mark in reasoning questions.

Exam tips

Draw the loop neatly with arrows showing the direction of traversal.
The ISC syllabus treats the B-H loop qualitatively: definitions and material choice matter most.
In choice questions, give the property and the reason in one sentence each.
List the three factors for electromagnet strength: current, turns per unit length, core permeability.

Practice questions on Hysteresis and Permanent Magnets

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
Soft iron is preferred for the core of an electromagnet because it has:
(a) low permeability and high retentivity
(b) high permeability and low retentivity
(c) high coercivity
(d) a wide hysteresis loop
Hint
Easy on, easy off.
Answer
(b).
Q2 · 1 mark · Very short answerBoard level
Define retentivity of a ferromagnetic material.
Hint
H back to zero.
Answer
The magnetic field (B) that remains in the material when the magnetising intensity is reduced to zero after saturation.
Q3 · 1 mark · Very short answerHarder board level
Explain why increasing the current in an electromagnet beyond a certain value hardly increases its field.
Hint
Domains.
Answer
The core saturates: nearly all domains are already aligned, so M cannot grow much more; only the small $μ_{0} H$ part keeps rising.
Q4 · 1 mark · Assertion-reasonHarder board level
Assertion (A): Steel is a suitable material for permanent magnets.
Reason (R): Steel has high coercivity, so a large reverse field is needed to demagnetise it.
(a) Both true, R explains A. (b) Both true, R does not explain A. (c) A true, R false. (d) A false, R true.
Hint
What must a permanent magnet resist?
Answer
(a).
Q5 · 2 marks · Short answerHarder board level
An electromagnet has 2500 turns per metre, carries 0.2 A and has a core of relative permeability 600. Find B.
Hint
$B = μ_{0} μ_{r} n I$ .
Answer
≈ 0.377 T.
Q6 · 2 marks · Short answerHOTS / competency
A transformer core of volume $2 \times 1 0^{- 3}$ m³ is made of a material whose hysteresis loop area corresponds to 250 J m⁻³ per cycle. Find the power lost at 50 Hz and the heat produced in one hour.
Hint
Area × volume × frequency.
Answer
25 W; $9.0 \times 1 0^{4}$ J per hour.
Q7 · 4 marks · Case-basedHOTS / competency
Case study: Suppose a student's measured B-H loop for a sample saturates at ±1.5 T, crosses the B-axis at ±1.1 T and the H-axis at ±60 A m⁻¹.
(i) What is its retentivity? (1 mark)
(ii) What is its coercivity? (1 mark)
(iii) Is it better suited to a permanent magnet or a transformer core? Explain. (1 mark)
(iv) What would the loop look like if the sample were tested above its Curie temperature? (1 mark)
Hint
Compare 60 A m⁻¹ with permanent-magnet values of thousands.
Answer
(i) 1.1 T. (ii) 60 A m⁻¹. (iii) A transformer (or electromagnet) core: the coercivity is very low and the loop narrow, so little energy is lost; it would not stay magnetised against stray fields. (iv) No loop: the material is paramagnetic, giving an almost straight line through the origin with very small slope.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Define coercivity.Show answer
The reverse magnetic intensity needed to reduce B to zero after saturation.
2.What does the area of the hysteresis loop represent?Show answer
Energy lost as heat per unit volume per cycle.
3.Material for a permanent magnet?Show answer
High retentivity and high coercivity (steel, alnico).
4.n = 1000 m⁻¹, I = 1 A, μr = 1000: B?Show answer
≈ 1.26 T.
5.Why are transformer cores made of soft iron?Show answer
Narrow loop (low hysteresis loss), high permeability and low coercivity.

Hysteresis and Permanent Magnets: frequently asked questions

Why does B lag behind H?

Domain walls get pinned by impurities and defects; once domains have rotated they do not all return when H is reduced, so some magnetisation remains.

Is soft iron really "soft"?

"Soft" refers to its magnetic behaviour: it is easy to magnetise and demagnetise. Mechanically it is ordinary iron with few impurities.

Why is the hysteresis loss important for transformers?

The core goes round the loop every cycle of the a.c. supply. Energy equal to the loop area times volume is lost each cycle, so a wide loop would heat the core and waste power.

How deeply is the B-H loop examined in ISC?

The 2027 syllabus treats the B-H loop, retentivity and coercive force qualitatively, along with electromagnets, the factors affecting their strength, and the selection of materials for temporary and permanent magnets and transformer cores.

How was this chapter tested recently?

Short questions on definitions of retentivity and coercivity, the choice of material for magnets and cores, and loop features are typical 1- to 2-mark items.