CHAP. VI] 



EXCITING AMPERE-TURNS 



111 



path in the air between two rectangular poles of an electromagnet 

 (Fig. 30). Assume the paths of the flux to consist of concentric 

 quadrants with the centers at c and c f j joined by parallel straight 

 lines, and let the width of the poles in the direction perpendicular 

 to the plane of the paper be h. Then the permeance of an infin- 

 itesimal layer of thickness dx, between one of the poles and the 

 plane MN of symmetry, is 



Integrating this expression between the limits o and 6 we find 



(P =1.84/i log (1.576/J -1-1) perms . . . . (57) 



(compare with prob. 24 in Chapter V, Art. 37). 



In applying this formula and Fig. 30 to the case of the flank 

 leakage between the pole shoes, h is the average radial height of 

 the pole shoe, 6 is equal to one- 

 half the width of the pole shoe, 

 and 2Z is the distance between 

 the two opposing pole-tips. 

 While the method evidently 

 gives only a crude approxi- 

 mation to the actual perme- 

 ance, formula (57) at least 

 fixes a lower limit to the per- 

 meance in question. 



(a) Between the flanks of 

 the pole cores. The conditions 

 are similar to those under (c), 

 so that the permeance is esti- 

 mated again on the basis of 

 formula (57) . The sides of the 

 two rectangles in Fig. 29 are 

 not parallel to each other as in 

 Fig. 30, but this difference is 

 taken into account by mentally 

 turning] them into a parallel 



position, and estimating the equivalent distance 21 between the 

 edges of the opposing poles. The dimension h is in this case the 

 radial height of the pole-waist, and b is one-half of tho width of 

 the pole-waist. The flank 1, akage is small.-!- than that between 



Fio. 30. The magnetic path between 

 the poles of an electromagnet. 



