The flux densities of the magnetic fields created in the air gap by each of the three stator currents of a three-phase 2-pole ac machine are given respectively for phases a, b, and c by the equations below, where alpaha is the angular position in the air gap (alpha = 0 corresponds to the phase a axis).
B a = B M cos(omega t) cos(alpha);
B b = B M cos [omega t - 2 pi/3) cos (alpha - 2 pi/d);
B c = B M cos (omega t + 2 pi/3) cos (alpha + 2 pi/3).
Each equation above describes a field that is distributed sinusoidally and whose amplitude varies sinusoidally with time (a pulsating field). Prove for the resultant magnetic flux density in the air gap (a) at any given t, the flux density is distributed sinusoidally with respect to alpha; and (b) the center of the flux rotates around the air gap at an angular velocity equal omega. That is, prove that B(t, alpha) = B a + B b, + B a = 2/3 BM cos(omega t - alpha).