Magnets and Motors
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. Eighteen drawn figures across twelve chapters.
12 chapters published
How to read this series
Each chapter starts in plain language and ends with real equations, worked examples and questions to test yourself. No prior background is assumed — but nothing is hand-waved either. Chapters build on each other, so reading in order pays off, though each is written to stand alone.
Part 1
The Physics of Magnetism
Where a magnetic field actually comes from, the three quantities engineers use interchangeably and should not, and the electrostatic effect — not a magnetic one — that holds a magnet together at all.
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.
A permanent magnet has no battery and no wire, so its field must come from electrons circulating and spinning inside atoms. This chapter separates the three quantities that describe the result — H the field you apply, M what the material contributes, B what actually exists and produces force — and shows why the distinction earns its keep: inside an open-circuit magnet, H and M point in opposite directions. That is the demagnetising field, and it is why a magnet’s shape changes its working point. Then where an atom’s moment comes from, and why magnetism lives in exactly two neighbourhoods of the periodic table.
Magnetic Dipoles Are Far Too Weak to Explain a Magnet
Treat two iron atoms as classical bar magnets and you predict an ordering temperature of about one kelvin. Iron stays magnetised to 1,043 K. Classical magnetism is wrong by three orders of magnitude.
What holds moments parallel is not magnetic at all — it is electrostatic, filtered through the Pauli principle. Parallel spins force an antisymmetric spatial wavefunction, which pushes electrons apart and lowers their Coulomb repulsion, so parallel is simply cheaper. The size and sign of that saving depend on interatomic spacing relative to orbital radius, and the Bethe–Slater curve shows how narrow the window is: manganese and chromium fall just left of zero and order antiparallel, iron cobalt and nickel just right of it. This chapter covers the five kinds of magnetic behaviour, the Curie temperature, and why Nd₂Fe₁₄B is a division of labour rather than a single clever material.
Part 2
The Permanent Magnet
The hysteresis loop as a complete specification, the anisotropy that makes a magnet permanent rather than merely magnetic, and the four material families that result — including the one whose coercivity moves the wrong way with temperature.
The Hysteresis Loop Is the Magnet’s Entire Specification
Remanence, coercivity, intrinsic coercivity and energy product — four numbers from one measurement. And a permanent magnet in service never leaves the second quadrant.
Drive a magnetic material around a full cycle of applied field and the shape of the loop tells you how strong the magnet is, how hard it is to destroy, and how much energy it can store per unit volume. This chapter defines B_r, H_cB, H_cJ and (BH)max precisely, shows why intrinsic coercivity is the number that matters for demagnetisation safety and is always the larger of the two, and calculates the theoretical ceiling for NdFeB — about 516 kJ/m³, against 398 to 422 for commercial N52, which means there is very little headroom left in the compound. Then the load line, an interactive second-quadrant curve, and the reversible-versus-irreversible distinction that costs warranties.
Anisotropy Is the Property That Makes a Magnet Permanent
Iron has a large moment and a high Curie temperature, and it is useless as a permanent magnet. What separates a magnet from a lump of ferromagnet is how firmly its magnetisation is anchored to a crystal direction.
Magnetocrystalline anisotropy arises from spin–orbit coupling: the spin is coupled to the orbital motion, the orbital shape is fixed to the lattice by the crystal field, and so the spin is indirectly bolted to the crystal. Spin–orbit coupling scales steeply with atomic number and the 4f charge cloud is strongly aspherical, which is why the answer is always a rare earth — iron’s K₁ is 0.048 MJ/m³ against Nd₂Fe₁₄B’s 4.9. Then Brown’s paradox, why every real magnet achieves only 15 to 30 per cent of its theoretical anisotropy field, why that makes coercivity a microstructure property rather than a chemistry one, and how grain boundary diffusion exploits exactly that.
The Magnet Families, and What Each One Is Actually For
Neodymium magnets are the strongest available, which is not the same as being the right answer. Ferrite outsells them by mass many times over, and one family’s coercivity moves the wrong way with temperature.
Four families compared on energy product, temperature capability and cost: sintered NdFeB, samarium cobalt, hard ferrite and AlNiCo. Each entry states what it is for and what its disqualifying flaw is — NdFeB corrodes and loses coercivity fast with temperature, SmCo gives up half its energy product to buy 350 °C, ferrite is a tenth the strength but costs almost nothing and has no eddy loss, and AlNiCo’s shape-based anisotropy makes it easy to demagnetise by accident. A full datasheet table follows, and one row in it contains the only positive temperature coefficient in the set: ferrite demagnetises when cold, which inverts every intuition built on neodymium.
Part 3
The Machine
How a traction motor makes torque two different ways at once, what is inside each rotor topology and what that choice commits you to, and the four loss mechanisms that each dominate somewhere different.
An EV Motor Makes Torque Two Different Ways at Once
The first term is current interacting with magnet flux. The second is free torque from geometry alone — available whether or not there is a magnet present, and worth 30 to 50 per cent of the total.
The torque equation has two terms, and the second is the one that shapes rotor design. Reluctance torque comes from magnetic asymmetry — flux takes the easiest path, so a rotor that is easy in one direction and hard in another is pulled into alignment. Building that asymmetry is the entire design of an interior-permanent-magnet rotor, and a surface-magnet rotor cannot do it. Then MTPA control, why the torque peak sits near 30 to 35 degrees of current angle rather than zero, the D²L scaling law that explains why traction motors are small and geared, the identity between torque and back-EMF constants, and field weakening — which is deliberately driving the magnets backwards at the moment the motor is hottest.
What Is Inside the Rotor Decides Everything Else
Every traction motor has essentially the same stator. The interesting choice — cost, efficiency, supply-chain exposure, controller complexity — is what spins inside it.
Six rotor topologies drawn to the same scale and compared on what they commit you to: IPM as the incumbent with the highest torque density and 1 to 2 kg of NdFeB, SPM as simpler and worse for traction, induction with no magnets and no supply exposure but rotor I²R loss by definition, EESM where field strength becomes an independent control variable, SynRM and its ferrite-assisted variant as the most credible rare-earth-free path, and axial flux for torque density. Then windings: why hairpin conductors replaced round wire, and the AC-loss catch that arrives with them at highway speed.
Four Loss Mechanisms, Each Dominant Somewhere Different
A traction motor at its best point converts 97 per cent of what it is given. The design problem is not that number — it is that the missing three per cent moves around.
Copper loss dominates at low speed where current is highest; iron and AC-copper loss dominate at high speed where frequency is highest; the efficiency island sits between them, which is why gear ratio selection is an efficiency decision rather than only a top-speed one. This chapter works through the thermal runaway hiding inside I²R, the skin-depth arithmetic that puts traction motors on the wrong side of the crossing for most of a highway cycle, the two iron-loss mechanisms and their different frequency laws, why rotating machines use non-oriented steel, magnet eddy loss and why segmentation exists, and the efficiency map — where urban driving sits in the worst region rather than the best.
Part 4
Limits and Supply
How rotors are actually destroyed — hot and reverse-driven at the same instant — why rare earths are not rare but separating them is, and the instruments that turn any of this from assertion into measurement.
Demagnetisation Needs Two Conditions at Once
A magnet does not weaken gradually toward failure. It performs to specification, and then at some combination of temperature and reverse field it crosses the knee and loses a permanent chunk in a fraction of a second.
The design case is not a hot day. It is a three-phase short circuit at high speed with the rotor already at maximum temperature — an inverter fault at the end of a long gradient, where the fault current is large, its field opposes the magnets directly, and the magnets are at their least resistant. A second case is aggressive field weakening, which applies a demagnetising field deliberately and continuously. This chapter shows the same magnet at three temperatures against one fixed load line and one fault field, then covers cooling methods in order of capability, why peak rating runs two to three times continuous, and the mismatch that shapes the whole design: Class H insulation tolerates 180 °C while an N42 magnet is finished at 80.
Rare Earths Are Not Rare. Separating Them Is the Problem.
Neodymium is more abundant in the crust than lead. Cerium is more abundant than copper. The name is an eighteenth-century accident, and only half of it is still true.
If price tracked abundance, the rare earths would fall on a line. They do not, because the cost is in separation rather than extraction. The lanthanide contraction means adjacent neighbours differ in ionic radius by roughly one per cent and all sit in the same +3 state, so separation relies on solvent extraction exploiting a partition coefficient that differs by a few per cent per stage — hundreds to over a thousand mixer-settler stages in cascade. That plant, its capital and its waste stream are the actual barrier, which is why opening a mine does not solve it. Then five approaches to reducing exposure, ranked by how proven they are, and why recycling a motor is a richer proposition than any ore.
Measuring Magnets and Motors
Almost every number in this series is measured on one of about ten instruments. Knowing which one produced a figure tells you how much to trust it.
Eleven instruments, what each measures and what it is really for — the hysteresigraph as the definitive test and the basis of incoming acceptance, VSM for milligram fragments a hysteresigraph cannot hold, Helmholtz coil and fluxmeter for fast 100 per cent production screening, back-EMF test as the single best health check on an assembled rotor, locked-rotor testing for the inductances the controller needs, the dynamometer where claimed efficiency becomes measured efficiency, and Kerr microscopy for the domain structure coercivity actually depends on. Closes with the two things worth demanding from any magnet or motor supplier.
Part 5
Reference
The whole argument compressed onto one page, with the datasheet numbers behind it.
More chapters are being written. Companion to The Periodic Table of the EV. Where that series covers why a cell is made of what it is made of, this one covers the other half of the powertrain.