THE MAGNETIC CIRCUITELECTROMAGNETS 31 

 therefore 



& a 



cos 



Also, since 



cos 2 cos 2 

 The same relation holds good for cone-shaped pole pieces. 

 Thus, referring to Fig. 13, in which the magnet core is supposed 

 to have a circular cross-section of radius r; 



FI = kBi 2 Ai = kBi 2 irr z for normal gap 



and 



FIG. 13. Magnet with conical pole faces. 

 F 2 = kB**A 2 X cos $ 



for conical gap; where the factor cos 6 is introduced as before 

 to obtain the axial component of the magnetic forces. 



The conical surface, which corresponds to the cross-sectional 

 area of the air gap, is, 



Also, for the same exciting ampere-turns, we have as before, 



cos0 



and, 



cos 2 

 Fi 



COS 2 



which is identical with formula (20). 



