30 



PRINCIPLES OF ELECTRICAL DESIGN 



squares of the densities taken over the various component areas 

 of the cross-section considered. This is briefly summed up in 

 the general expression, 



pull, in dynes = oi I B 2 dA 



Pull between Inclined Surfaces. Conical Plungers. Sketch 

 (a) of Fig. 12 shows a portion of an electromagnet of rectangular 

 cross-section, with air gap (of length I) normal to the direction 

 of movement. The sketch (6) shows a similar bar of iron, but 

 with the air gap inclined at an angle with the normal cross- 

 section. The total movement, which is supposed to be confined 

 to the direction parallel to the length of the bar, is the same in 

 both cases; that is to say, the air gap measured in the direction 



() v 



FIG. 12. Magnet with inclined air gap. 



of motion, has the same value, I, although the actual air gap 

 measured normally to the polar surfaces is smaller in (6) than 

 in (a). The magnetic pull will actually be exerted in a direction 

 normal to the opposing surfaces, that is to say, in the direction 

 OF, in case (6), although it is the mechanical force exerted in 

 the direction OF% which it is proposed to calculate. 



For the perpendicular gap (sketch a) we can write, 



total longitudinal force FI = kBi 2 Ai (18) 



where k is a constant. 



For the inclined gap (sketch 6); 



total longitudinal force F 2 = kB 2 2 A 2 X cos 8 (19) 

 Now express equation (19) in terms of A\ and B\. With the 

 ampere-turns of constant value, and considering the reluctance 

 of the air gap only, the flux density will be inversely proportional 

 to the shortest distance between the two parallel surfaces. 

 Thus, 



fo OC r 



Zcos e 



