Three-Phase Induction Motor: Rotating Field & Slip

Supply & Machine

Supply frequency f 50 Hz

Pole pairs p 2

Supply voltage V 220 V

Load torque T_load 4.0 N·m

⚠ Stalled — load exceeds breakdown torque

Live Readouts

Sync. speed n_s

1500 rpm

Rotor speed n

0 rpm

Slip s

100 %

Torque T

0.0 N·m

Breakdown T_max

— N·m

Rotor freq. f₂=sf

— Hz

How it works

Three stator windings 120° apart, fed with currents 120° out of phase, produce a magnetic field of constant magnitude that rotates at the synchronous speed:

n_s = 60·f / p   (rpm)
ω_s = 2π·n_s / 60  (mechanical rad/s)

This rotating field sweeps past the rotor conductors, inducing currents in them (Faraday's law) which, by the Lorentz force, drag the rotor around — but it can never quite catch up, or no relative motion (and so no induced current) would remain. The gap is the slip:

s = (n_s − n) / n_s        n = n_s(1 − s)
f₂ = s·f    (frequency of the induced rotor currents)

Torque comes from the classic induction-motor equivalent circuit (stator resistance/leakage R₁,X₁, rotor resistance/leakage referred R₂,X₂):

T(s) = 3·V² · (R₂/s) / { ω_s · [ (R₁ + R₂/s)² + (X₁+X₂)² ] }

At standstill (s=1) this gives a finite starting torque; as s→0 torque→0. In between it rises to a peak — the breakdown torque T_max at s_max = R₂/√(R₁²+(X₁+X₂)²) — then falls. The simulator solves T(s) = T_load for the stable operating slip (the rising branch, 0 < s ≤ s_max) every time you move a slider, and eases the rotor toward that speed the way real rotor inertia would. If the load exceeds T_max, the rotor cannot find a stable point and stalls (s = 1).

Frequency / pole pairs — set the synchronous speed n_s the field spins at.
Voltage — torque scales with V², so a small voltage sag costs a lot of torque.
Load torque — the mechanical load the shaft must overcome; higher load needs more slip to generate matching torque.

This is exactly how the induction motors in pumps, fans, conveyors and most industrial drives work — no brushes, no permanent magnets, just a traveling magnetic field and Faraday's law.

Rotating stator field Rotor (cage bars) Phase U · V · W

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