SINE WAVE OF FLUX 



37 



forces is made to act across the gap, producing in it a multipolar field, 



so that the direction of the flux is alternately from stator to rotor and 



rotor to stator. The distribution 



of this flux is generally more or 



less irregular, and depends on 



the particular arrangement of the 



windings, the discontinuities in 



tin- polar surfaces of the cores, 



etc. Now, just as in considering 



alternating e.m.f.'s and currents 



we made no attempt to deal with 



the numerous wave-shapes which 



occur in practice, but confined 



our attention to the simplest 



possible wave the pure sine 



wave so in the present instance, 



instead of dealing with the more Fm 27 _ T of Alteroating ^ uwent 



or less irregular distribution of Machine. 



the magnetic flux which occurs 



in practice, we shall select for special treatment the simplest case 



of all that, namely, in which the magnetic flux is distributed in 



the air-gap according to the simple sine law. If the distance x be 



measured along the circumference of the rotor (Fig. 28), and if we 



select for our origin a point at which the magnetic field vanishes or 



STATOR 



ROTO R 

 FIQ. 28. Simple Sine Wave of Flux. 



changes sign, then according to the above supposition the value of the 

 magnetic induction y at any point of the gap distant x from the origin 

 may be represented by 



y = & sin qx (1) 



