In one line
When a balanced three-phase current flows in three stator windings placed 120° apart in space, the combined flux has constant magnitude (1.5 times the peak flux of one phase) and rotates at synchronous speed \( N_s = 120f/P \).
Explained simply
Think of three spotlights placed around a stage, switched on and off one after another in sequence. The bright spot seems to move round the stage even though no light moves. The three stator windings are like those spotlights: each phase's flux peaks in turn, so the resultant field appears to rotate smoothly.
Technically, the three phase fluxes are \( \phi_R = \phi_m\sin\omega t \), \( \phi_Y = \phi_m\sin(\omega t - 120^\circ) \), \( \phi_B = \phi_m\sin(\omega t - 240^\circ) \), acting along axes 120° apart. Adding them as vectors at any instant gives a resultant \( 1.5\phi_m \) whose direction advances with time.
How it works
- At \( \omega t = 0^\circ \): \( \phi_R = 0 \), \( \phi_Y = -0.866\phi_m \), \( \phi_B = +0.866\phi_m \). Vector sum \( = 2\times0.866\phi_m\cos30^\circ = 1.5\phi_m \).
- At \( 60^\circ \), \( 120^\circ \), \( 180^\circ \): the resultant is still \( 1.5\phi_m \) but has turned by the same angle in space (for a 2-pole winding).
- So the field rotates once per cycle for a 2-pole winding; for \( P \) poles it rotates at \( 120f/P \) rpm.
- Interchanging any two supply lines reverses the phase sequence and hence the direction of rotation.
Key formula
\( N_s = \dfrac{120f}{P}, \qquad \phi_r = 1.5\phi_m \)
\( N_s \) = synchronous speed (rpm), \( f \) = supply frequency (Hz), \( P \) = number of stator poles, \( \phi_r \) = resultant flux (Wb), \( \phi_m \) = peak flux of one phase (Wb).
Quick example
At 50 Hz: a 2-pole stator gives \( N_s = 3000 \) rpm, 4-pole gives 1500 rpm, 6-pole gives 1000 rpm. That is why most common induction motors on Indian nameplates run a little below 3000, 1500 or 1000 rpm.
Common mistakes
- Saying the resultant flux pulsates; with balanced three-phase supply it is constant in magnitude.
- Writing the resultant as \( 3\phi_m \) or \( \phi_m \); it is \( 1.5\phi_m \).
- Thinking the rotor creates the rotating field.
How MU asks it
Numericals are not expected in this module (as per the MU syllabus), so questions are theory. Typical: "Explain the production of a rotating magnetic field in a three-phase induction motor" (5–8 marks). For full marks draw the three flux waveforms, choose at least three instants (e.g. 0°, 60°, 120°), draw the vector sum at each, show \( 1.5\phi_m \) each time, and state \( N_s = 120f/P \) and the method of reversal.