The idea. An induction motor has no brushes and no commutator. The stator (the part that does not move) has three sets of coils, A, B and C, with their axes 120° apart. They are connected to the three phases of the supply, whose currents are the same size but peak one third of a cycle apart:

i_A = I₀ cos ωt, i_B = I₀ cos (ωt − 120°), i_C = I₀ cos (ωt − 240°)

Each coil makes a field along its own axis that is proportional to its current. Adding the three field vectors (turn on “Show the field of each coil”) gives a total field of constant strength, 1.5 times the peak field of one coil, pointing at angle ωt. So the field rotates once per cycle of the supply: the synchronous speed is n_s = 60f/p rpm for p pairs of poles. On a 50 Hz supply a 2-pole motor has a field that turns at 3000 rpm, and a 4-pole motor at 1500 rpm.

Why the rotor turns. The rotor is a cage of aluminium or copper bars with nothing connected to them. The rotating field sweeps past the bars, so the flux through each loop of the cage changes. By Faraday’s law an EMF is induced, and because the cage is a closed circuit with a very low resistance, large currents flow in the bars. By Lenz’s law the force on those currents opposes the change that makes them: it drags the rotor in the direction the field is turning.

Slip. The rotor can never quite reach the speed of the field. If it did, the bars would not cut the field, there would be no EMF and no current, and so no torque. The difference is the slip:

slip s = (n_s − n) / n_s

The more load you put on the motor, the more the rotor lags, the bigger the EMF and the current in the bars, and the bigger the torque, until the torque balances the load. The graph shows the torque against speed. At normal loads the slip is only a few per cent. If the load is bigger than the pull-out torque (the top of the curve, about 2.5 times the rated torque here) the rotor cannot keep up, slows down and stalls.

Why three phases. With a single phase the field does not rotate. It just pulses back and forth along one line, which is the same as two fields of half the size rotating in opposite directions. At standstill the two torques cancel exactly, so a single-phase induction motor cannot start (try “Needs three phases”, then “Give the rotor a push”). Real single-phase motors use a starting trick, such as a capacitor, to make a second, shifted phase. Swapping two phases makes the field turn the other way, and the motor reverses.

The model. The torque curve is T = T_max 2 s s_m / (s² + s_m²), with the pull-out torque T_max = 2.5 times the rated torque and the slip at pull-out s_m = 0.25 (so the starting torque is about 1.2 times the rated torque). The speed follows from the rotor’s inertia and the difference between the motor torque and the load. The picture is a 2-pole motor, shown from the end. Real stators have many more coils and slots, the rotor bars are slanted, and the iron core is laminated.

Things to try. (1) With the supply on and no load, how close to the field speed does the rotor get? (2) Increase the load slowly. What happens to the slip and to the currents in the bars? (3) Find the load at which the motor stalls. (4) Swap two phases while it runs. (5) Why does a motor draw a very large current when it starts?