CHAP. II] MAGNETIC CIRCUIT WITH IRON 27 



estimating it from the results of previous tests, rather than to 

 calculate it theoretically. 



Prob. 1. Samples of cast steel are to be tested for their magnetic 

 quality up to a density of 19 kilolines per square centimeter. They are 

 to be in the form of rings, 20 cm. average diameter, and 0.75 sq.cm. 

 cross-section. For how many ampere-turns should the exciting winding 

 be designed, and what is the lowest permeance of the circuit, if some 

 specimens are expected to have a permeability 10 percent lower than 

 that according to the curve in Fig. 2? A 



Ans. 10.\kiloampere-turns; 1.37 perm. 



Prob. 2. Explain the reason for which it is not necessary to know the 

 cross-section of the specimens in order to calculate the necessary ampere- 

 turns in the preceding problem. 



Prob. 3. Some silicon steel laminations are to be tested in the form of 

 a rectangular bunch 20 by 2 by 1 cm., in an apparatus called a permeam- 

 eter. The net cross-section of the iron is 90 per cent of that of the 

 packet. It is found for a sample that 336 ampere-turns are required to 

 produce a flux of 25.2 kilo-maxwells, the ampere-turns for the air-gaps and 

 for the connecting yoke of the apparatus being eliminated. How does 

 the quality of the specimen compare with the curve in Fig. 3? 



Ans. The permeability of the sample at B = 14 is about 5 per cent 

 lower than that according to the curve. 



Prob. 4. What are the values of the absolute and the relative per- 

 meability and reluctivity of the sample in the preceding problem? 



Ans. ft v 



relative 663 (numeric) 0.00151 (nuni. 



absolute 833 perms per cm. cube 0.00120 rels per cm. cube. 



Prob. 6. What is the maximum permeability of cast iron according to 

 the curve in Fig. 2? Ans. About 600 perms per cm. cube. 



Prob. 6. Mark in Figs. 2 and 3 vertical scale- of :iltsolu(eand n ! 

 permeability, so that values of permeability could he read off directly 1>> 

 laying a straight edge between the origin and the desired point of the 

 magnetization < in 



Prob. 7. What is the percentage of saturation in carl>on steel lamina- 

 tions at a flux density of 20 kilo- maxwells per square centi 

 according to txjth definitions piven in Art. 12? Ans. 92.5; 88.5. 



Prob. 8. An electromagnet has the dimensions (in cm.' >h..\vn in 



' the -ore is made of carbon steel laminations 1 mm. thick, the 



lower yoke is of cast iron. The lenpth of ea< -h li - mm.; each 



;> coil has 450 turn-. \Vh.-it H the exciting useful 



flux o! -/dines in the lower yoke? Neglect the magnetic leakage 



en the liml>- < 



rration in the next pml,lem>. Solution: With laminations 4 mm. thick 



ice occupied i,v insulation between stampings \B altogether negligi- 

 l.le; -he Hu\ densit \ in i he steel is the tame as in the air-gap 



and is equal to 17.2 kl/sq. cm.; in the cast iron the flux density is 1 1 .:. 



