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Rotating field in 3-phase IM

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.

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.

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°):

ωtφ_Rφ_Yφ_BResultant (axis of R = 0°, Y = 120°, B = 240°)
0°0−0.866 φ_m+0.866 φ_m1.5 φ_m at −90°
60°+0.866 φ_m−0.866 φ_m01.5 φ_m at −30°
120°+0.866 φ_m0−0.866 φ_m1.5 φ_m at +30°
180°0+0.866 φ_m−0.866 φ_m1.5 φ_m at +90°
         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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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