### Introduction

A rotating magnetic field is a particular magnetic field created by using coils with multiple electrical phases.

image credits  - science directi.com

### Mathematical Analysis of Rotating Magnetic Field

Usually, to create a rotating magnetic field, you’d have to physically spin a magnet or a coil, which requires an external force.

let’s consider a 3-phase, 2-pole stator with three windings: aa’, bb’, and cc’, spaced 120 degrees apart, and supplied with a 3-phase AC supply.

image credits  - Research gate

(1) At the very beginning (0⁰) (2) A bit later (60⁰) (3) Then, at 120⁰ (4) Finally, at 180⁰

### four different moments in time

image credits  - unplash

## When θ = 0⁰

i) When θ = 0⁰ (At point 0) : At point 0 on the waveform i.e., at 0⁰, the value of Φ1 is,

### When θ = 60⁰ (At point 1)

At point 1 on the waveform i.e., at 60⁰, the value of Φ1. Since Φ3 = 0, the resultant of Φ1 and Φ2 can be found by reversing Φ2 and adding it with Φ1

image credits  - unplash

At point 2 on the waveform i.e., at 120⁰. Since Φ2 = 0, the resultant of Φ1 and Φ3 can be found by reversing Φ3 and adding it with Φ1

### When θ = 120⁰ (At point 2)

At point 3 on the waveform i.e., at 180⁰. Since Φ1 = 0, the resultant of Φ2 and Φ3 can be found by reversing Φ3 and adding it with Φ2.

### Condition for Generation of Rotating Magnetic Field

Imagine you have three coils, labeled a, b, and c, and they’re all lined up so their magnetic directions point in the same way.