THE MAGNETIC CIRCUIT ELECTROMAGNETS 19 



The arrangement shown in Fig. 5 is supposed to represent a 

 steel casting consisting of the magnetic paths (1) and (2) in 

 parallel, with the common path (3) in series with them. It 

 will be seen that the paths (1) and (2) are provided with air gaps 

 and that the exciting coil is on the common limb (3) only. 

 Paths (1) and (3) have iron in them and the permeance of these 

 paths will depend upon the density B and therefore on the total 

 flux $1 and $ 3 in these portions of the circuit. In regard to path 

 (2), it also consists mainly of iron, but the cross-section of the 

 iron has purposely been made large, so that the reluctance of 

 this path is practically all in the gap; the value of B in the iron 

 will be very low, /* will be large, and the reluctance of this part 

 of the iron circuit will be considered negligible. The dimensions 





VsLfiX// / 



^-^ / 



FIG. 5. Typical magnetic circuit. 



of the parts are indicated on the sketch, and the problem to be 

 solved is the calculation of the necessary ampere-turns in the coil 

 to produce a given total flux of, say, 1,000,000 maxwells through 

 the path (1). 



The reluctance of path (1) alone consists of the air-gap reluc- 

 tance in series with the reluctance of the iron limb of length h 

 and cross-section A\. Thus, 



_ 



l ~ A g X 1 Ai X 



all dimensions being expressed in centimeters. The only 

 unknown quantity is MI, and this can be determined because the 

 flux density in the iron will be 



B'\ = = 1 ' 000 ' 000 = 100,000 maxwells per square inch, 



AI 1U 



