## Rotating Magnetic Field

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# Rotating Magnetic Field (Principal of an ac induction motors)

If there are two coils placed at right angles to each other carrying ac currents of the same peak value and frequency but differing in phase by π/2, they give rise to a rotating magnetic field. A rotating magnetic field is one in which the magnetic flux rotates round a fixed axis. Its magnitude remains while the direction changes at a constant rate.Consider two coils AD and EC placed at right angles to each other. Let i1 and i2 be the instantaneous values of the ac currents in the two coils. Let i0 be the peak value of the current.

Let i1 lead i2 bye π/2. Then

i

_{1}= i

_{0}sin [ωt + π2]

and i

_{2}= i

_{0}sin ωt

The magnetic fields produced by these currents are also at right angles to each other. The strength of each magnetic field is proportional to the current flowing through the respective coils at that instant. Let B1 and B2 be the instantaneous magnetic flux densities produced by the current i1 and i¬2 respectively.

Let B0 be the maximum flux density due to any one coil. Then,

B

_{1}= B

_{0}sin [ωt + π2] = B

_{0}cos ωt

And B

_{2}= B

_{0}sin ωt

Let the flux densities B1 and B2 be represented by the vectors OA and OC respectively. The resultant flux density B is then represented by the vector OR.

Or B = √B

^{2}

_{1}+ B

^{2}

_{2}= √ B

^{2}

_{0}cos2 ωt + B

^{2}

_{0}sin2 ωt

B = B

_{0}

Let the resultant magnetic flux density B make an angle θ with the direction of B1. Then,

tan θ = B

^{2}/B

^{1}= B

_{0}sin ωt/B

_{0}cos ωt

or θ = ωt Hence, the resultant magnetic flux density is always constant in magnitude (=B

_{0}) and rotates with constant angular velocity ω

Thus, the direction of the resultant magnetic flux density B rotates with a constant angular velocity ω about a fixed through O in the clockwise direction. Such a magnetic field is called a rotating magnetic field. If the current i

_{2}leads i1 by π/2, the magnetic filed rotates in the anticlockwise direction.

If now a conductor is placed at O in a rotating magnetic field, an induced e.m.f. is produced in it by the rotating field. According to Lenz’s law, the conductor will begin to move in the direction of the rotating field so that the relative velocity between the two may become the least.

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