Rotating Magnetic Field
Part of Generators and Motors
How spatially distributed windings carrying phase-shifted currents produce a magnetic field that rotates in space, enabling self-starting AC motors.
Why This Matters
The rotating magnetic field is the key invention that made AC motors practical. Before Nikola Tesla and Galileo Ferraris independently discovered it in 1887, AC motors did not work well — they needed mechanical starting, produced poor torque, and behaved unpredictably. The rotating field explained why, and its proper implementation enabled the smooth, self-starting induction motor that powers modern industry.
Understanding the rotating field is essential for winding multi-phase motors, diagnosing motor problems, and designing power systems that provide the right phase relationships for motor loads. It also explains phenomena like the phase sequence requirement for motors (connecting phases in the wrong order reverses the motor), and why single-phase motors need capacitors to start.
For a rebuilding civilization, this knowledge is the bridge between having AC power and being able to use that power to run machines reliably and efficiently.
Creating a Rotating Field with Two Phases
The simplest rotating field requires two sinusoidal currents equal in magnitude but displaced 90° in time, flowing in windings displaced 90° in physical space. Consider a stator with two winding sets (A and B) at right angles to each other.
Phase A current: IA = I × sin(ωt) — peaks in the north-south direction at t = 0 Phase B current: IB = I × cos(ωt) = I × sin(ωt + 90°) — displaced 90° from phase A
At t = 0: IA is maximum, IB is zero. The combined field points north-south. At t = T/4 (quarter cycle): IA is zero, IB is maximum. The combined field points east-west. At t = T/2: IA is maximum negative. The combined field points south-north.
The combined field sweeps continuously around the stator bore, completing one full rotation per electrical cycle. For a 50 Hz supply, the field rotates at 50 revolutions per second = 3,000 RPM for a 2-pole machine.
The magnitude of the combined field is constant: |F| = √(IA² + IB²) = I × √(sin²(ωt) + cos²(ωt)) = I (constant). This is the key property: the rotating field from balanced two-phase currents has constant magnitude and rotating direction — unlike a pulsating single-phase field, which oscillates in one direction.
Three-Phase Rotating Field: The Industrial Standard
Three-phase power uses three windings displaced 120° in space, carrying currents displaced 120° in time. The analysis is similar to two-phase: the vector sum of the three magnetic fields at any instant produces a resultant that has constant magnitude and rotates at the electrical frequency.
Why three phases instead of two? Three-phase distribution requires only three conductors (two-phase AC requires four for a complete two-phase supply). Three-phase is the most efficient multi-phase system: it delivers maximum power with minimum wire for a given voltage and current level. It also produces a smoother rotating field with lower harmonic distortion than two-phase.
The three-phase rotating field speed is: Ns = 120 × f / P (RPM), where f is frequency and P is pole count. For 50 Hz, 2 poles: Ns = 3000 RPM. For 50 Hz, 4 poles: Ns = 1500 RPM. For 50 Hz, 6 poles: Ns = 1000 RPM.
The pole count determines the physical arrangement of the stator windings. A 4-pole stator has two north poles and two south poles arranged alternately around the bore. The winding for each phase has coils in multiple positions so the total field pattern has four poles at any given instant.
Phase Sequence and Motor Direction
The rotating field rotates in the direction determined by the sequence in which the phases reach their peak: A-B-C in one direction, A-C-B in the other. This is the phase sequence. Phase sequence determines which way an induction motor turns.
For a motor connected to a three-phase supply and running in the correct direction, swapping any two of the three supply leads reverses the phase sequence and the motor reverses direction. This is the standard method for reversing an induction motor — no mechanical changes needed, just swap two of the three feed wires at the motor terminal block.
For a generator being synchronized to a bus, phase sequence must match before closing the parallel breaker. If the phase sequences are opposite, closing the breaker is equivalent to a dead short — the two generators are 180° out of phase and will try to reverse each other. A phase sequence indicator (a simple instrument) or the voltage-across-switch method (measure voltage across the open breaker: it should go to zero at synchronization moment) verifies that phase sequences match.
Single-Phase Rotating Field: Why It Doesn’t Work Naturally
A single-phase winding produces a pulsating field, not a rotating one. The field oscillates sinusoidally between maximum north and maximum south in one direction only. This can be decomposed mathematically into two rotating fields of half magnitude spinning in opposite directions. The forward-rotating component creates forward torque; the backward-rotating component creates reverse torque of equal magnitude. At standstill, they cancel exactly — net starting torque is zero.
Once the motor is rotating, the rotor reacts differently to the forward and backward components (it is in phase with one and out of phase with the other), and the net torque becomes positive in the direction of rotation. This is why a single-phase motor given a physical push will run, but cannot start itself — it has no net starting torque at zero speed.
Single-phase motor starting solutions all create a temporary two-phase condition:
Capacitor-start: a capacitor in series with a start winding shifts the current in the start winding by approximately 90° relative to the main winding. This creates an approximate rotating field, sufficient for starting. A centrifugal switch disconnects the start winding (and capacitor) once the motor reaches about 75% of synchronous speed. The motor then runs on the single-phase supply alone.
Capacitor-start capacitor-run: two capacitors — a large one switched out after starting, and a small running capacitor that stays in circuit. The running capacitor improves power factor and running efficiency.
Shaded-pole motors: a shading band of copper on part of each pole face creates a phase-shifted flux component, producing a weak rotating field. Very simple and cheap, but low efficiency and limited torque. Used in fans and small appliances where simplicity matters more than efficiency.
Verifying Rotating Field Direction in Practice
Before connecting a motor to load, verify it turns the right direction and will not damage driven machinery (pumps, fans, and compressors can be damaged or simply fail to pump if run backwards).
Method: run the motor briefly with no load (or disconnect from the load) and observe rotation direction. Compare to the required direction of the driven machine.
If direction is wrong: swap any two of the three supply leads at the motor terminal box. Do not swap at the motor’s internal terminals — the terminal box is where the connections should be changed.
For a single-phase motor: reverse direction by reversing the start winding connections relative to the main winding. Most single-phase motors have terminal markings that allow this. Some motors are not reversible (the start winding is not externally accessible) — these must be used in one direction only.
Building Stators for Rotating Field Generation
When winding a three-phase stator by hand, spatial accuracy of the winding placement is critical. An error in the angular placement of a winding set shifts the time phase of that phase’s contribution to the rotating field, resulting in an asymmetric rotation (the field speed is not constant — it speeds up and slows down within each cycle, which causes torque pulsations in the motor).
Measure the angular position of each slot carefully when laying out the winding pattern. Mark the slot positions on the stator laminations before winding begins. Use a protractor or dividing head for accuracy. For a 36-slot, 4-pole, 3-phase stator: each slot pitch is 360°/36 = 10°. The winding for phase A occupies slots 1, 4, 7, etc. (every third slot). Phase B occupies slots 2, 5, 8, etc. Phase C occupies 3, 6, 9, etc. This achieves the required 120° electrical displacement between phases (each physical slot equals 20° electrical for a 4-pole machine).
After winding, verify the phase displacement by connecting one phase to a known AC source, rotating the shaft by hand, and measuring the voltage induced in each of the other phases. The peaks should be displaced by one-third of a full rotation of the shaft (for a 2-pole machine) or one-sixth of full rotation (for a 4-pole machine). If they are not, the winding placement has an error to diagnose and correct before the machine goes into service.