---
title: "Rotating field in 3-phase IM"
subject: "Electrical Machine"
chapter: 5
key: "semester_4/electrical_machine:rotating-field-3ph-im-vector"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/rotating-field-3ph-im-vector
site: BCT Engineering
---

# Rotating field in 3-phase IM

Electrical Machine · Chapter 5: Three Phase Induction Machines

- Asked in: 2071 Bhadra, 8 marks
- Video: [Production of Rotating Magnetic Field (RMF) in 3 Phase Induction Motor](https://www.youtube.com/watch?v=XaNFrpzACe0) — Lectures in Electrical Engineering by Muni Sankar
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/rotating-field-3ph-im-vector
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-5

## Question

Explain with necessary vector diagram how rotating magnetic field is produced in a three phase induction motor. Also explain how this rotating magnetic field helps the motor to rotate.

## Short answer

Three-phase currents 120° apart in time flow through windings 120° apart in space, producing a constant-magnitude resultant flux (1.5 φ_m) rotating at N_s=120f/P rpm. This rotating field cuts rotor conductors, inducing emf and currents; Lenz's-law forces create torque that tries to eliminate relative motion, so the rotor rotates in the same direction at N < N_s.

## Answer

When a balanced three-phase supply is given to a three-phase stator winding placed 120° apart in space, the three pulsating fluxes combine into one flux of constant magnitude that rotates at synchronous speed. This is the rotating magnetic field (RMF).

#### Production of the RMF
Let the three phase fluxes (each along its own winding axis, 120° apart) be

- φ_R = φ_m sin ωt
- φ_Y = φ_m sin (ωt − 120°)
- φ_B = φ_m sin (ωt − 240°)

Take the instants below and add the three fluxes as vectors (axes of R, Y, B windings at 0°, 120°, 240°):

| ωt | φ_R | φ_Y | φ_B | Resultant (axis of R = 0°, Y = 120°, B = 240°) |
|---|---|---|---|---|
| 0° | 0 | −0.866 φ_m | +0.866 φ_m | 1.5 φ_m at −90° |
| 60° | +0.866 φ_m | −0.866 φ_m | 0 | 1.5 φ_m at −30° |
| 120° | +0.866 φ_m | 0 | −0.866 φ_m | 1.5 φ_m at +30° |
| 180° | 0 | +0.866 φ_m | −0.866 φ_m | 1.5 φ_m at +90° |

```text
         R axis (0°) ->
 ωt=0 : resultant points at -90°
 ωt=60: resultant points at -30°   (turned +60°)
 ωt=120: resultant points at +30°  (turned +60°)
 ωt=180: resultant points at +90°  (turned +60°)

 The length stays 1.5 φm; the direction turns 60° for
 every 60° of the supply cycle, i.e. one revolution per
 cycle for a 2-pole winding.
```
Mathematically, the resultant flux is

**φ_r = (3/2) φ_m**, constant in magnitude, rotating at

**N_s = 120 f / P rpm** (f = supply frequency in Hz, P = number of poles).

The direction of rotation follows the phase sequence. Interchanging any two supply lines reverses it.

#### How the RMF makes the rotor turn
1. The RMF rotates at N_s and cuts the stationary rotor conductors.
2. By Faraday's law, an emf is induced in the rotor conductors. The rotor bars are short-circuited (cage) or closed through the slip rings, so rotor currents flow.
3. A current-carrying conductor in a magnetic field experiences a force (F = BIl). These forces on all conductors produce a torque on the rotor.
4. By Lenz's law, the direction of the force is such that it opposes the cause of the induced current, that is, the relative speed between the field and the rotor. The rotor therefore tries to follow the RMF, and it rotates in the same direction.
5. The rotor can never reach N_s. If N = N_s there is no relative speed, no emf, no current and no torque. So the rotor runs at N < N_s, and the difference is the slip:

**s = (N_s − N) / N_s**

This is why the machine is called an asynchronous or induction machine: the rotor current is produced by induction, with no electrical connection to the supply.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the magnitude of the resultant flux?
   A. 1.5 φ_m
   B. 3 φ_m
   C. 0.5 φ_m
   D. φ_m
   Answer: A. Three fluxes combine into constant 1.5 φ_m. (Key point: Resultant flux)

2. At what speed does it rotate?
   A. N_s = 60f
   B. N_s = 120f/P
   C. N_s = f/P
   D. N_s = 120P/f
   Answer: B. Synchronous speed. (Key point: Speed)

3. How is the direction of rotation reversed?
   A. Change frequency
   B. Remove one phase
   C. Interchange any two supply lines
   D. Increase voltage
   Answer: C. Phase sequence determines direction. (Key point: Reversal)

4. How does the field make the rotor turn?
   A. It attracts permanent magnets
   B. It reduces slip to zero
   C. It heats the rotor
   D. It induces rotor current whose force follows the field, by Lenz's law
   Answer: D. Induced currents experience forces; the rotor follows the field but stays below N_s. (Key point: Torque)

## Related in Electrical Machine

- [Production of rotating magnetic field](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Arotating-magnetic-field-production) — Electrical Machines, chapter 5
- [Rotating magnetic field, slip and standstill torque equation](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Armf-synchronous-speed-slip-standstill-torque) — Electrical Machines I, chapter 5
- [Synchronous speed; rotor follows rotating field](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Asynchronous-speed-rotor-direction) — Electrical Machines, chapter 5
- [Split phase induction motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Asplit-phase-im) — Electrical Machine, chapter 7
- [Construction and working of 3-phase induction motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ainduction-motor-construction-working) — Electrical Machines I, chapter 5
- [Operating principle of 3-phase induction motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ainduction-motor-operating-principle) — Electrical Machines I, chapter 5

## Related in other subjects

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- [DFRT and equivalent circuit of single phase IM](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Adfrt-equivalent-circuit) — Electric Machines II, chapter 3
- [Variable frequency control of induction motor](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Ainduction-motor-variable-frequency-control) — Utilization of Electrical Energy, chapter 3
- [Scalar vs vector magnetic potential](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Ascalar-vs-vector-magnetic-potential) — Electromagnetism, chapter 3, asked 4×