CHAP. VI] 



EXCITING AMPERE-TURNS 



115 



Prob. 15. Let AB and CD (Fig. 31) represent the cross-sections 

 of two opposite pole-faces of an electromagnet, inclined at an angle 20 

 to one another. Show that of the three assumptions with regard to the 

 shape of the lines of force in the air between the poles (a) is more correct 

 than (6) and (6) is more correct than (c); in other words, the assumption 

 (a) gives a higher permeance than (6) or (c). Hint : tan > > sin 0. 



Prob. 16. Show that the permeance according to Fig. 31a, between 

 one of the faces and the plane MN of symmetry, is equal to 



where h is the width of the pole-faces perpendicular to the plane of the 

 paper, and that formulae (56) and (57) are special cases of it. 



Prob. 17. The formula given in the preceding problem is deduced 

 under the assumption that the same m.m.f. is acting on all the lines of 



(<*) 



(c) 



Fio. 31. The magnetic paths l>otwecn the poles of an electromagnet (three 



assumptions). 



force. Let now Fig. 31a represent a cross-section of two opposing pole 

 cores in an electric machine, the m.m.f. hot wren .1 and C bein^: 

 and uniformly increasing to a value M between the joints B and I). 

 Show that the equivalent permeance of the path, referred to the m.in.f. 

 M is equal to (/iA/0)[l- (J/to)fi(to/I+l)], 



NOTE. If it is desired to use regularly the foregoing formula in esti- 

 mating the leakage factor, the values of the expression in the In 

 [ ] can be plotted as a curve for the values of (l/Ow) as abscissir. Similar 

 formula- can le deduced and curves plotted for the permeance of the 

 flank leakage between adjacent |>oles. The path* of the lines of force 

 he poles can be assumed to trie <|iiadrants and between 



the (x>les to have a shape similar to that indicated in Fig. 31a. 



41. The Permeance and Reluctance of Irregular Paths. In 

 using the methods described al>ove for the calculation of the 

 ampere- mm- for the air-gap, the teeth, and the cores, and in esti- 



