258 THE MAGNETIC CIRCUIT [ART. 72 



uniformly over the armature periphery, so that the stored mag- 

 netic energy is the same in all positions of the armature. It 

 would be entirely wrong, however, to apply this formula to 

 a slotted armature, using for B the actual small flux density 

 in the slot within which the conductor lies. This would give 

 the force acting upon the conductor itself, and tending to press 

 it against the adjacent conductor or against the side of the slot; 

 but the actual tangential force exerted upon the armature as 

 a whole is many times greater, and practically all of it is exerted 

 directly upon the steel laminations of the teeth. 



At no-load, the flux distribution in the active layer of the 

 machine is symmetrical with respect to the center line of each 

 pole (Fig. 24), so that the resultant pull along the lines of force 

 is directed radially. The armature currents distort the field 

 as a whole, and also distort it locally around each tooth, the 

 general character of distortion being shown in Fig. 36. The 

 unbalanced pull along the lines of force has a tangential com- 

 ponent which produces the armature torque. This torque, 

 although caused by the current in the armature conductors, 

 is largely exerted directly upon the teeth, because the flux density 

 there is much higher. 



Thus, in order to determine the total electromagnetic torque 

 in a slotted armature, it is again necessary to apply the principle 

 of virtual displacements. The reluctance of the active layer 

 per pole varies somewhat with the position of the armature, 

 so that the energy stored in the field is also slightly fluctuating. 

 It is convenient, therefore, to take a displacement which s a 

 multiple of the tooth pitch, in order to have the same stored 

 energy in the two extreme positions. This gives the average 

 electromagnetic torque. 



(a) The Torque in a Direct-current Machine. Let the virtual 

 displacement be equal to geometric degrees and be accomplished 

 in t seconds. Then we have 



(195) 



where T is the torque, i is the total armature current, and E is 

 the total induced e.m.f. Eq. (195) states the equality of the 

 mechanical work done and of the corresponding electrical energy 

 supplied. The average induced e.m.f. is independent of the 

 flux distribution, or of the presence or absence of teeth (see 



