FR, FY and FB represent the mmfs of the three phases, while currents in them are at their positive peak values. Each of the phases current is alternating sinusoid ally with time. As the currents alternate, the mmfs of the three phases shall vary in magnitude and change direction so as to follow modify in current.
The air gap mmf at any angle, θ, is because of contribution by all of the three phases. Let the angle θ be measured from the axis of phase R. The resultant mmf at angle θ is
Fθ = [FR (peak ) cos θ + FY (peak ) cos (θ - 120o ) + FB (peak ) cos (θ + 120o )]
Beginning from the instant while current in phase R is at its maximum value, we have
FR (Peak) = FR (max) cos ωt
Fy (Peak) = Fy (max) cos (ωt - 120o)
FB (Peak) = FB (max) cos (ωt + 120o)
For balanced currents,
FR (max) = Fy (max) = FB (max) = Fmax
Substituting the values from Eqs. (29), (30) and (31) into Eq. (29), we have
F (θ, t ) = Fmax cos ωt cos θ + Fmax cos (ωt - 120o ) cos (θ - 120o )+ Fmax cos (ωt + 12) cos (θ + 120)
Solving the Eq. we have
F (θ, t ) = 1.5 Fmax cos (θ - ωt )
The resultant mmf wave given by Eq. (33) contains a constant magnitude. The term (ωt) gives rotation of mmf around the air gap at constant angular velocity ω. The angular velocity of the wave is ω = 2 π f electrical radians per second.