The field that turns without anything moving
In rungs 1 and 2 you met the DC motor: feed current to a coil, it sits in a magnet's field, torque pushes it round, and the spinning coil pushes back with a back-EMF. It works, but it needs brushes and a commutator — sliding contacts that wear out, spark, and need replacing. Tesla's great insight in the 1880s was to ask: what if the *field itself* could rotate, so the rotor never needs an electrical connection at all? Then the messy sliding contacts simply vanish.
Here is the trick, and it is pure geometry. Take three coils and space them 120° apart around the inside of a steel ring — the stator. Feed them the three currents of a three-phase AC supply, which themselves peak 120° apart in time. At any instant the three coils make three magnetic fields pointing in three directions, and when you add those vectors the resultant is a single field of constant strength that points in a steadily rotating direction. Nothing mechanical moves, yet the magnetic north pole sweeps smoothly around the ring, once per electrical cycle.
Three stator coils 120° apart, fed by three currents 120° apart:
ωt = 0° ωt = 90° ωt = 180°
N ↗ N S
| / |
───●─── → ───●─── → ───●───
| / |
S S ↙ N
The RESULTANT field (■) keeps the same magnitude
but its DIRECTION rotates at synchronous speed:
n_s = 120 · f / P (revolutions per minute)
f = supply frequency (Hz)
P = number of stator POLES (always even: 2, 4, 6, …)Faraday drags the rotor along
Now drop a rotor into the middle of that whirling field. The rotor is just bars of conductor — no power feed, no permanent magnet. As the stator field sweeps past, each rotor bar sees a *changing* magnetic field, and by Faraday's law a changing field induces a voltage. That induced voltage drives a current through the rotor bars. You now have current-carrying conductors sitting inside a magnetic field — exactly the recipe for force. The field pushes on those rotor currents and produces torque, and the rotor begins to turn, chasing the field that created it.
This is why the machine is called an *induction* motor: the rotor current is induced by the stator field, never wired in. The rotor is, in effect, the secondary of a rotating transformer — which is why an older name for it is the *rotary transformer*. Lenz's law tells you the direction: the induced rotor current opposes the change that made it, which means it tries to 'catch up' to the field and reduce the relative motion. That very attempt is the torque that spins your pump.
Slip: why the rotor must always lose the race
Here is the subtle, beautiful constraint at the heart of the machine. The rotor chases the rotating field — but it can never quite catch it. Suppose for a moment it did, spinning at exactly synchronous speed. Then the rotor bars would move *with* the field, see no changing flux, induce no voltage, carry no current, and feel no force. With no torque the rotor would immediately fall behind again. So the rotor is condemned to run slightly slower than the field, forever. That lag is slip.
Slip s = (n_s − n_r) / n_s (a fraction, often a %)
n_s = synchronous speed (the field)
n_r = actual rotor speed (the shaft)
s = 1 → rotor stopped (standstill / starting)
s = 0 → rotor at synchronous speed (impossible under load:
no slip ⇒ no torque)
typical running slip: s ≈ 0.01 … 0.05 (1 %–5 %)
Rotor (slip) frequency: f_r = s · f
— the frequency of the voltage & current INDUCED in the rotor.Slip is the regulating signal of the whole machine. Put more load on the shaft and the rotor slows a touch; slip rises; the rotor bars now cut the field faster, so a larger voltage is induced, a larger current flows, and more torque is produced — automatically — until it matches the new load. The motor self-regulates with no controller at all. A healthy four-pole 50 Hz motor whose field spins at 1500 rpm will typically settle around 1440–1470 rpm at full load: a slip of just 2–4%.
The torque–slip curve: start, pull-out, and the operating sweet spot
Plot the torque a motor produces against its slip and you get the single most useful picture in machine design. Read it from right to left — from standstill (s = 1) toward synchronous speed (s = 0). At standstill the motor makes its starting torque: enough to break away and accelerate the load, but not its maximum. As the rotor speeds up and slip falls, torque climbs to a peak — the pull-out or breakdown torque, the most the motor can ever deliver. Push past that peak (load it too hard) and torque *falls*, the motor stalls, and current soars dangerously.
Torque ^ ___ pull-out / breakdown torque (T_max) | / \ | starting / \ | torque • / \ | / \__/ \ | / \ ← stable operating region | / \ (steep, near-vertical) | / \ | / \ +--+------------------+---------+----------------> slip s=1 (standstill) T_max s≈0.03 s=0 (n_s) start ~0.15–0.2 RUN POINT no torque Full load sits on the STEEP part near s=0: a big torque change needs only a tiny speed change.
The genius is in *where* the motor settles. Normal full-load operation sits on the steep, almost-vertical stretch just to the left of pull-out, at only a few percent slip. On that steep slope an enormous change in torque demands only a tiny change in speed — so the motor holds its speed nearly rock-steady from no load to full load, the way a stiff spring barely stretches under load. That stiffness is exactly what a saw, a conveyor or a lathe wants. Stray onto the shallow part past pull-out, though, and the motor cannot recover: it stalls.
A worked example: slip, rotor frequency and the full load point
Numbers make this concrete. Take a common workhorse: a 4-pole, three-phase induction motor on a 50 Hz supply, with a nameplate full-load speed of 1455 rpm. Two quick calculations — synchronous speed and slip — tell you almost everything about its working state, including the slip frequency that explains its start-up behaviour and the speed at which it actually drives the load.
GIVEN: 4-pole, 3-phase, f = 50 Hz, full-load speed n_r = 1455 rpm
STEP 1 — Synchronous speed (the field's speed):
n_s = 120 · f / P = 120 · 50 / 4 = 1500 rpm
STEP 2 — Slip at full load:
s = (n_s − n_r) / n_s = (1500 − 1455) / 1500
= 45 / 1500 = 0.03 → 3 %
STEP 3 — Rotor (slip) frequency:
f_r = s · f = 0.03 · 50 Hz = 1.5 Hz
(so the rotor bars carry a slow 1.5 Hz current at full load)
STEP 4 — Compare with STANDSTILL (s = 1, the instant of starting):
f_r,start = 1 · 50 = 50 Hz → full-frequency, big inrush current
SANITY CHECK: rotor lags the field by 1500 − 1455 = 45 rpm.
That 45-rpm gap is the entire source of the motor's torque.- Find synchronous speed first: n_s = 120·f / P. Get the pole count P right — it is always even, and counts poles, not pole-pairs.
- Compute slip s = (n_s − n_r) / n_s. A healthy full-load slip is a small fraction — 1–5%; a value near zero means almost no load, near 1 means stalled.
- Get the rotor frequency f_r = s·f. This is the frequency seen *inside* the rotor — tiny at run, full at start.
- Interpret it physically: low running slip ⇒ good efficiency; the standstill case (s = 1) is why direct-on-line starting causes a large inrush.
The squirrel cage: cheap, rugged, and why it rules industry
Open up the rotor that all this torque acts on and you find one of engineering's great pieces of minimalist design: the squirrel cage. There are no coils, no windings, no insulation to fail. It is simply a stack of laminated steel discs with conducting bars — usually cast aluminium, sometimes copper — running through slots near the surface, all short-circuited at both ends by two solid conducting rings. Strip away the steel and the bare conductor looks exactly like a hamster's exercise wheel, which is where the name comes from.
That simplicity is the whole commercial story. With no brushes, no commutator, no slip rings and no magnets, a squirrel-cage motor has almost nothing to wear out — the only consumables are two bearings. It is sealed against dust and moisture, costs a fraction of any alternative, tolerates overloads, and runs for decades. There is no electrical connection to the rotor at all, so there is nothing to spark in an explosive atmosphere. This is why it became, and remains, the default electric motor of civilisation.
SQUIRREL-CAGE ROTOR (cutaway, end view + side view): end view side view ___ ┌───────────────┐ end ring / · \ · = conductor │ ║ ║ ║ ║ ║ ║ ║ │ ← bars in slots |· ●● ·| bars around │ ║ ║ ║ ║ ║ ║ ║ │ (slightly skewed) |·● ●·| a steel core └───────────────┘ end ring \ ·· / shaft in mid bars SHORTED by both end rings ‾‾‾ → induced current circulates freely No windings • no brushes • no slip rings • no magnets Just bars + 2 shorting rings + laminated steel.
The induction motor's one historic weakness was speed control — its speed is locked near synchronous speed by the supply frequency, so for a century it ran flat-out or not at all. The fix was the variable-frequency drive: power electronics that synthesise a three-phase supply of *adjustable* frequency, sliding the synchronous speed up and down at will. Pair a rugged squirrel cage with a modern drive and you get a machine that is cheap, indestructible and fully speed-controllable — which is why even electric trains and EV-class motors lean on this 140-year-old idea. The cousin that runs at exactly synchronous speed with zero slip — the synchronous machine — is the subject of the next rung.