CHAP. VI] 



EXCITING AMPERE-TURNS 



119 



Prob. 19. For some ratio of slot width to air-gap draw the tooth- 

 fringe field to the perpendicular surface of the pole, adjust the number 

 and spacing of the lines of force by Dr. Lehmann's method, and see how 

 closely you can check the corresponding point on Carter's curve (Fig. 26). 



Prob. 20. From the given drawing of a machine, determine the 

 permeance of the fringe from the pole-tip to the armature by Lehmann's 

 method; consult, if necessary, Dr. Lehmann's original article. 



Prob. 21. Map out the leakage field between the opposing pole-tips 

 ami cores of a given machine, and determine its equivalent permeance by 

 Lehmann's method, assuming the field coils to be thin and close to the core. 



41a. The Law of Flux Refraction. When mapping out a field 

 in air, the lines of force must be drawn so as to enter the adjoining 

 iron almost normally to its surface, even if they are continued in 

 the iron almost parallel to its surface. The lines of force change 

 their direction at the dividing surface suddenly (Fig. 32), and in 

 so doing they obey the so-called law of flux refraction; namely, 



tan 0</tan 0^ 



(58) 



Equlpol '"'' 



surfaces 



lrn 



Since fa is many times smaller than /,-, the angle 6 a is usually very 

 small, unless 0,- is very nearly 90 degrees. It may be said in gen- 

 eral that the lower the permeability 

 of a medium the nearer the lines 

 of force are to the normal at its 

 limiting surfaces. In this way, the 

 path between two given points is 

 shortened in the medium of lower 

 permeability and is lengthened in 

 the medium of higher permeability. 

 Thus, the total permeance of the 

 circuit is made a maximum. 



To deduce* the above-stated law 

 of refraction, consider a tube of 

 flux between the equipotential sur- 

 faces ab and cd, the width of the 

 path in the direction perpendicular 

 to the plane of the paper being one 

 cditiiiHtn. Let Bi and B a be the 

 flux densities, and //, and //., tin* 



magnetic inn unties in the two media. Two 

 must be satisfied, namrl\ . first, the drop of ni.m.f. 



Fio. 32. The refraction of 

 a flux. 





