258 ELECTRICAL ENGINEERING 



The second term represents a constant demagnetizing effect and 

 the last term is a double-frequency quantity. 



If the air-gap length is so adjusted that its permeance varies 

 according to a sine law from a maximum ^o under the centre of a 

 pole to zero, midway between poles, Fig. 237, its equation is 



2 = % sin 6 (248) 



The flux density in the gap at any angle 6 is 



t - ^ gin 0) sin 0+^sin (20-0) sin 01 

 lines per sq. cm (249) 



FIG. 237. 



The flux cut per second by the two sides of the coil is 2 S&lv lines, 

 where I is the length of conductor under the pole in cm. and v is 

 the velocity in cm. per sec. 



Thus the e.m.f. generated in the coil of n turns is 

 6 = 2 mvn 10- 8 = KZ& volts, 



where K = 2 lvnlO~ 8 is a constant, 

 or substituting for 9$ 



e = 



(u f - ^y sin 0) sin + ^- sin (20-0) sin \ 



- ^y sin Ain0 + ^Jcos (0 - 0) - cos (3 0- 0) jl 

 , - ^ sin 0) sin + ^- \ sin sin 

 + cos 6 cos cos (3 B 0) I I 



/-^ sin <fi\ sin (9 +^cos <j> cos 0- ^ cos^3 e -0) j 



= U sin (9 + ^ cos - C cos (3 (9- 0)} ...... (250) 



where A, B and C are constants. 



