What a Magnetic Field Actually Is
There is no magnetic charge. Every field in the universe comes from moving electric charge — and B, H and M are three different quantities that people use interchangeably and should not.
Magnets and Motors · Part 1 — The Physics of Magnetism · Chapter 1 · 18 min read
Part 1 — The Physics of Magnetism
Before the machine, the field
Every magnetic field in the universe comes from moving electric charge. A permanent magnet has no wire, so its field must come from somewhere else.
A traction motor is one idea executed well: make a magnetic field rotate, and put something magnetic inside it. Everything else — the alloy, the lamination, the winding, the cooling — is a consequence of that.
This chapter is about the first half of the sentence, and specifically about three quantities that engineers use interchangeably and should not.
B = μ₀(H + M)
The relationship worth memorising
9.274×10⁻²⁴
J/T — the Bohr magneton
2.22 μ_B
Iron’s moment per atom
10.6 μ_B
Dysprosium’s — and it makes a worse magnet
1.1 — There is no magnetic charge
Electric charge comes in isolated units. Magnetic charge does not. Cut a bar magnet in half and you get two magnets, each with a north and a south; there is no such thing as a lone north pole.
Every magnetic field in the universe therefore comes from moving electric charge — a current in a wire, or an electron circulating and spinning inside an atom.
In plain English
A permanent magnet has no battery and no wire, so its field must come from the second kind. Each atom carries a tiny current loop, and in a magnet those loops are aligned instead of randomised. That is the whole trick. The rest of this series is about what makes the alignment happen, what makes it stay, and what happens when it stops.
1.2 — H, M and B — three quantities, not one
- •H — magnetic field strength (A/m). What you apply. Set by the current you push through a coil and the geometry: for a long solenoid, H = NI/ℓ. It exists independently of what material is present.
- •M — magnetisation (A/m). What the material contributes — the net magnetic moment per unit volume of the material itself. Zero in air, enormous in iron.
- •B — magnetic flux density (tesla). What actually exists in the material, and the quantity that produces force. This is what a Hall probe reads and what appears in every force and torque equation.
B = μ₀(H + M)
μ₀ = 4π × 10⁻⁷ H/m, the permeability of free space.
1.3 — Why the distinction earns its keep
Important
A magnet in an open circuit has H and M pointing in opposite directions inside itself. The magnet’s own poles create a field that pushes back against its own magnetisation — the demagnetising field.
That is not a curiosity. It is why a magnet’s shape changes its working point, why a long thin magnet sits high on its curve near remanence while a short flat one sits low, and why an identical magnet performs differently in two motors.
Why this matters later
It is also the reason the load line exists at all, which is the subject of chapter 3 — and the reason a magnet quoted at 1.4 T on a datasheet delivers considerably less in a real airgap.
1.4 — Where an atom’s moment comes from
An electron contributes magnetic moment two ways: orbital angular momentum, its circulation around the nucleus, and spin, which is intrinsic and has no classical analogue.
The natural unit is the Bohr magneton, μ_B = 9.274 × 10⁻²⁴ J/T — the moment of a single unpaired electron spin.
μ = −g · μ_B · J
g = Landé factor · J = total angular momentum quantum number. Hund’s rules fix J: maximise total spin S first, then total orbital L, then couple them as J = |L−S| below half filling and J = L+S above it.
That is why Dy³⁺ (4f⁹, J = 15/2) reaches 10.6 μ_B while iron manages 2.22.
1.5 — Why magnetism lives in two neighbourhoods
Paired electrons cancel. So an atom has a net moment only if it has unpaired electrons, which in practice means a partially filled d or f shell. That confines magnetism to exactly two regions of the periodic table, and nowhere else.
Technical framing
Read that chart and note the inversion it sets up. Dysprosium carries nearly five times iron’s moment — and nobody builds a magnet out of dysprosium, while iron is in every magnet worth having.
Big moment and useful magnet are different things. The 4f column wins on moment and loses on exchange, because buried 4f orbitals barely overlap between neighbouring atoms. Chapter 2 is that story, and it is why every practical magnet pairs one element from each column.
Quick check: test yourself
1.A Hall probe reads 0.9 T in an airgap. Which of B, H and M is that, and why does it matter?
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2.Why does an identical magnet deliver less flux in one motor than another?
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3.Copper has 29 electrons. Why is it not magnetic?
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Chapter summary
- ✓There is no magnetic charge. Every field comes from moving charge — in a permanent magnet, from aligned atomic current loops rather than a wire.
- ✓H is what you apply, M is what the material contributes, B = μ₀(H + M) is what exists and produces force. They are not interchangeable.
- ✓Inside an open-circuit magnet H opposes M. That demagnetising field is why shape changes a magnet’s working point, and it is the origin of the load line.
- ✓An atom has a moment only if it has unpaired electrons, which confines magnetism to partially filled d and f shells.
- ✓The 4f elements carry the largest moments and make the worst magnets on their own — moment and useful magnet are different properties.
Frequently asked questions
What is the difference between B, H and M?+
H is magnetic field strength in A/m — what you apply, set by the current through a coil and the geometry, and it exists independently of any material. M is magnetisation in A/m — what the material itself contributes, zero in air and enormous in iron. B is magnetic flux density in tesla — what actually exists in the material and the quantity that produces force, related by B = μ₀(H + M). A Hall probe reads B, and B is what appears in every torque equation.
What is the demagnetising field?+
Inside an open-circuit magnet, H and M point in opposite directions: the magnet’s own poles create a field that pushes back against its own magnetisation. That is not a curiosity — it is why a long thin magnet sits high on its curve near remanence while a short flat one sits low, why an identical magnet performs differently in two motors, and why the load line exists at all.
Why are only some elements magnetic?+
Because paired electrons cancel, so an atom has a net moment only if it has unpaired electrons — which in practice means a partially filled d or f shell. That confines magnetism to two neighbourhoods of the periodic table and nowhere else. The natural unit is the Bohr magneton, μ_B = 9.274 × 10⁻²⁴ J/T, the moment of a single unpaired electron spin.
Why does dysprosium carry a bigger moment than iron but make a worse magnet?+
Because moment and useful magnet are different properties. Dy³⁺ (4f⁹, J = 15/2) reaches about 10.6 μ_B against iron’s 2.22, since Hund’s rules maximise spin then orbital angular momentum in a deeply buried shell. But those buried 4f orbitals barely overlap between neighbouring atoms, so the exchange coupling that holds moments parallel is weak — which is the subject of chapter 2, and why every practical magnet pairs a 3d element with a 4f one.
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Magnets and Motors is an original educational series on permanent magnets and electric machines. Datasheet ranges, temperature coefficients and efficiency figures are representative standard-condition literature values, not measurements of a specific product, and sources differ on several. Always verify against the specific magnet and lamination datasheets in use before making design, procurement or certification decisions.