38 ALTERNATING CURRENTS 



The distribution of the flux may be graphically represented as in 

 Fig. 28, where the values of y are laid off, to a convenient scale, along 

 lines perpendicular to the rotor circumference. 



We may speak of the distance A which separates two correspond- 

 ing points on the curve of induction, and within which are included 

 all possible values of the induction, as the magnetic wave-length. The 

 wave-length clearly corresponds to the distance between the middle 

 points of two pole-pieces of the same name, or to twice the pole-pitch. 

 Since the substitution of x + X for x leaves y unaltered as regards 

 both magnitude and sign, we must have 



or 



sin qx = sin (qx + q\] 



N . 2ir 



qX = 2-jr, i.e. q = - 



Equation (1) and the corresponding curve of Fig. 28 give the 

 distribution of the flux at a given instant, with a given current cir- 

 culating around the coils which produce the m.m.f.'s.* Now, let us 

 suppose that the current is alternating, so that the magnetic p.d. 

 across the gap at any given point on the rotor circumference varies 



X-0 



FIG. 29. Oscillations of Simple Alternating Wave. 



according to the simple harmonic law with the time. Then & in 

 equation (1) will no longer be a constant, but will be represented by 



b = B sin pt 

 where p = -~, T being the period. 



* M.m.f. = magnetomotive force. 



