**rotating magnetic field in 3 phase induction motor**, which is produced by the stator winding in the air gap between in the stator and the rotor. The stator has a three phase stationary winding which can be either star connected or delta connected.

Whenever the AC supply is connected to the stator windings, line currents

*I*

_{R},

*I*

_{Y}, and

*I*

_{B}start flowing. These line currents have phase difference of 120

^{o}with respect to each other. Due to each line current, a sinusoidal flux is produced in the air gap. These fluxes have the same frequency as that of the line currents, and they also have the same phase difference of 120

^{o}with respect to each other.

Let the flux produced by the line currents

*I*

_{R},

*I*

_{B},

*I*

_{Y}be φ

_{R}, φ

_{B}, φ

_{Y}respectively.

Mathematically, they are represented as follows:

φ

_{R }= φ

_{m}sin ωt = φ

_{m}sin θ

φ

_{B}= φ

_{m}sin (ωt – 120

^{o}) = φ

_{m}sin (θ – 120

^{o})

φ

_{Y}= φ

_{m}sin (ωt – 240

^{o}) = φ

_{m}sin (θ – 240

^{o})

The effective or total flux (ɸ

_{T}) in the air gap is equal to the phasor sum of the three components of fluxes ɸ

_{R}, ɸ

_{Y}and, ɸ

_{B}.

Therefore, ɸ

_{T}= ɸ

_{R}+ ɸ

_{Y}+ ɸ

_{B}

## Prove that RMF in Induction Motor is Rotating

To prove that this RMF is rotating we will:

**Step 1**: We will find the values of total flux ɸ_{T} for different values of θ such as 0, 60, 120 , 180 ….. 360^{o}.

**Step 2**: For every value of θ in step 1, we will draw the phasor diagrams.

By observing these phasor digrams you can understand easily that ɸ

_{T}keep shifting its position from 90^{o}to 30^{o}to – 30^{o}to – 90^{o}and so on. In other words ɸ_{T}rotates in the clock wise direction.

We will use the phasor ɸ_{R} as the reference phasor i.e. all the angles are drawn with respect to this phasor.

## ɸ_{T} at θ = 0^{o}

## ɸ_{T} at θ = 60^{o}

## ɸ_{T} at θ =120^{o}

## ɸ_{T} at θ =180^{o}

Similarly we can prove that ɸ_{T} at θ =180^{o} is given by,

ɸ_{T} = 1.5ɸ_{m} ∠ – 90^{o}

The phasor diagram for θ =180^{o} is shown in Figure (d).

## Speed of Rotating Magnetic Field in Induction Motor

The magnetic field in three phase induction motor (RMF) rotates at a constant speed called **synchronous speed (Ns)**, which is given by,

N_{S} = 120f_{1}/P RPM

where f_{1} = Frequency of stator supply

P = Number of poles of motor.

## Direction of Rotating Magnetic Field

The direction of rotating magnetic field depends upon the phase sequence of the AC supply connected across the stator winding. If we interchange any two phases of the AC supply, we will get new phase sequence, then the direction of *rotating magnetic field in three phase induction motor* will reverse. It will start rotating in reverse direction and so does the rotor.

**Since a stator and its winding of three phase induction motor is the same as that of a synchronous motor. So all above discussion about RMF in induction motor is the same for RMF in synchronous motor also.**

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