Five box faces have combined outward flux +f. What is the remaining face’s outward flux?

−f. The fluxes must sum to zero across the complete closed surface.

The distant axial field is B. What is it at twice that distance?

B/8. The distance factor is cubed: doubling gives a factor of eight.

A freely turning magnet points opposite a uniform field. What follows a small turn from opposition?

It turns farther from opposition. Turning towards alignment lowers its potential energy.

The same magnetic moment occupies half the volume. What happens to magnetisation?

It doubles. Dividing the same moment by half the volume doubles magnetisation.

A linear material has zero susceptibility. What is its relative permeability?

One. Zero material response still leaves the vacuum contribution.

Which nearby pole weakly repels a diamagnetic sample?

Either pole. Reversing the field also reverses the sample’s induced moment.

An unsaturated paramagnet warms in a fixed weak field. What happens to its magnetisation?

It decreases. Greater thermal disorder weakens the field’s partial alignment of atomic moments.

Before the field was applied, were the individual domains already magnetised?

Yes. Each domain already contains aligned atomic moments.

Teach Magnetism and Matter in eight steps.

For each idea: show it, ask before you tell, then say one line.

Gather paper and a pencil.

Common misconceptions & worked visual for this chapter · 15 practice questions with answers

Why it matters

A compass needle turns because a magnetic field can turn a magnet.
A magnet attracts an iron needle where the field varies.
Soft iron readily loses magnetisation, making it useful in switched electromagnets.

What to teach

How to teach it

Magnets and their fields

Magnetic field loops cross a dashed boundary around a bar magnet.

1. Magnetic poles and Gauss’s law

Entering and leaving magnetic flux balance.

Show: Find the diagram’s magnet and trace both field loops through it. Find where each loop enters and leaves the dashed boundary. The boundary represents a closed surface.
Ask: If we move this closed boundary, will entering and leaving magnetic flux still balance?
Say: Entering and leaving flux balance; the field remains.
Used in: A compass makes the local field’s direction visible.

If your child says…“Zero total flux means there’s no field.”

Ask: Does balancing the crossings erase either loop?
What’s true: Equal entering and leaving flux can cancel even where the field is strong.

Equal-distance axial and equatorial points show opposite field directions and different strengths.

2. Axial and equatorial dipole fields

Far away, a magnet’s field weakens with distance cubed.

Show: Find the axial point beyond the magnet’s end in the diagram. Find the equally distant equatorial point above its centre.
Ask: How would the field change moving from this end position to this side position?
Say: Far away, the axial field follows the magnetic moment, from south towards north. The equally distant equatorial field points oppositely and is half as strong.
Used in: Magnetic door alarms detect the weakening field as doors open.

If your child says…“Twice as far means one-quarter of the field.”

Ask: What fraction remains when the distance factor is multiplied three times?
What’s true: A short magnet’s distant field decreases with the cube of distance.

Tilted, aligned and opposed magnetic moments in the same uniform field.

3. Torque and magnetic potential energy

Fields turn magnets towards a stable, lower-energy alignment.

Show: Find the diagram’s tilted magnetic moment arrow, then the aligned and opposed arrows. Follow the curved torque arrow towards alignment.
Ask: Which position would the magnet return towards after a small turn?
Say: Alignment has minimum energy and is stable. Opposition also has zero torque, but a small turn carries it farther away.
Used in: A permanent magnet helped orient a satellite using Earth’s magnetic field.

If your child says…“Zero torque means it must be stable.”

Ask: After a nudge from opposition, does turning towards alignment lower its energy?
What’s true: Both aligned and opposed positions have zero torque, but only alignment gives stable equilibrium.

Describing a material’s response

Two samples have equal magnetisation above a material-filled ideal long solenoid.

4. Magnetisation and magnetic intensity

Magnetisation is magnetic moment per volume.

Show: Compare each sample’s volume, V, and magnetic moment, m, in the diagram. Below, find the material inside the ideal long solenoid.
Ask: Would doubling this sample’s volume and moment increase its magnetisation?
Say: Magnetisation stays equal because moment and volume increase together.
Used in: An electromagnet’s iron core strengthens its field, helping cranes lift iron.

If your child says…“I multiply moment by volume to get magnetisation.”

Ask: Does doubling both moment and volume change the moment in each unit of volume?
What’s true: Magnetisation measures the net moment in each unit of volume.

$\mu_r=1+\chi_m$

$\mu_r=1+0.02$

5. Susceptibility and permeability

Relative permeability compares material and vacuum fields at equal magnetic intensity.

Show: Use a linear material with susceptibility 0.02. Name μᵣ relative permeability and χₘ susceptibility. Say, “Relative permeability includes the vacuum contribution plus the material’s response.” Write the relationship after your child predicts.
Ask: What relative permeability includes both the vacuum field and this material’s extra response?
Say: Relative permeability compares the total field with the vacuum field. The vacuum contributes one, and the material adds its susceptibility, giving 1.02.
Used in: A transformer’s permeable core helps transfer energy between coils.

If your child says…“Relative permeability is just susceptibility.”

Ask: If the material adds nothing, does the vacuum field disappear?
What’s true: Relative permeability includes the vacuum contribution as well as the material’s response.

How materials respond

Diamagnetic moments appear only with an applied field and oppose either field direction.

6. Diamagnetism

An applied field induces an opposing magnetic moment.

Show: Find the field-off sample in the diagram. Compare the induced moments under the rightward and leftward fields.
Ask: Will this sample respond when the field switches on, despite having no permanent atomic moments?
Say: The field induces opposing moments even without permanent atomic moments. They reverse with the field and disappear when it is removed.
Used in: Superconducting shields exclude magnetic fields, protecting sensitive instruments.

If your child says…“One pole repels it, so the other attracts it.”

Ask: When the field reverses, what happens to the moment it induces?
What’s true: The induced moment changes direction with the applied field, preserving the opposing response.

Equal atomic moments show less overall alignment in the warmer paramagnetic sample.

7. Paramagnetism and thermal disorder

Heat disrupts the partial alignment of permanent atomic moments.

Show: Compare the cooler and warmer samples in the diagram. Check their equal applied fields and equal-length atomic moment arrows.
Ask: How would warming change this sample’s magnetisation in the same field?
Say: Warming weakens magnetisation because thermal motion disrupts alignment. The atoms keep their permanent moments.
Used in: Oxygen analysers use oxygen’s weak magnetic attraction to measure its proportion in a gas.

If your child says…“Heating helps the tiny magnets line up.”

Ask: Would more random motion help the moments keep a shared direction?
What’s true: Heating weakens magnetisation while the material remains paramagnetic and unsaturated in a fixed weak field.

Domains change during magnetisation and retain some overall alignment after the field is removed.

8. Ferromagnetic domains and remanence

Magnetised domains can cancel; some materials retain their overall alignment.

Show: Find the domains before magnetisation in the diagram. Follow their changes during the applied field and after its removal.
Ask: After removing the field shown here, must this sample lose all its magnetisation?
Say: Domains already contain aligned atomic moments, but their contributions can cancel. The field favours domains pointing along it. Here, some magnetisation remains after removal.
Used in: Hard magnetic materials retain magnetisation, making them useful as permanent magnets.

If your child says…“An unmagnetised nail has no magnetised regions.”

Ask: Could magnetised regions point differently and cancel when taken together?
What’s true: An applied field can favour existing domains without creating their magnetisation from nothing.

A real problem

A permanent magnet helped stabilise a satellite.

Swayam was developed by the College of Engineering, Pune.

Its stabilisation design used a permanent magnet aligned with Earth’s magnetic field.

Satellite data indicated that stabilisation occurred on 30 June 2016.

ISRO’s U R Rao Satellite Centre Maharashtra Directorate of Technical Education

A magnetic compass resting on a wooden classroom desk.

Concept Lab · Common misconception

The tempting mistake in Magnetism and Matter

Open standalone misconception page →

Can you separate the north pole by cutting a magnet?

Wrong

Cutting a bar magnet in half gives one north pole and one south pole.

Why it feels right. The original poles are at opposite ends.

Right

Each ordinary fragment remains a dipole with its own north and south poles.

Worked example

Before

NOne barS

After

NPiece 1S

NPiece 2S

Cutting creates new faces with opposite poles. Each piece remains a dipole.

Cut across a bar magnet.
Each shorter bar has an original end and a new cut end.
A compass can distinguish the opposite poles on each bar.

Ask your child eight quick questions.

One per step. The answer and the reason are given.

Five box faces have combined outward flux +f. What is the remaining face’s outward flux?

−f. The fluxes must sum to zero across the complete closed surface.
The distant axial field is B. What is it at twice that distance?

$\frac{B}{8}$ . The distance factor is cubed: doubling gives a factor of eight.
A freely turning magnet points opposite a uniform field. What follows a small turn from opposition?

It turns farther from opposition. Turning towards alignment lowers its potential energy.
The same magnetic moment occupies half the volume. What happens to magnetisation?

It doubles. Dividing the same moment by half the volume doubles magnetisation.
A linear material has zero susceptibility. What is its relative permeability?

One. Zero material response still leaves the vacuum contribution.
Which nearby pole weakly repels a diamagnetic sample?

Either pole. Reversing the field also reverses the sample’s induced moment.
An unsaturated paramagnet warms in a fixed weak field. What happens to its magnetisation?

It decreases. Greater thermal disorder weakens the field’s partial alignment of atomic moments.
Before the field was applied, were the individual domains already magnetised?

Yes. Each domain already contains aligned atomic moments.

15 more questions with answers, 1 with pictures

Teach Magnetism and Matter in eight steps.

Why it matters