48 'HIE MAGNETIC CIRCUIT [ART. 20 



Note: All parts of the core and all the teeth are subjected to complete 

 cycles of magnetization in succession; therefore, in calculating the core 

 lo<< the total volume of the core and of the teeth must be multiplied l>v 

 the loss per cubic decimeter, corresponding to the maximum magnetic 

 density in each part. 'The density in a tooth varies along its length, 

 being a maximum at the tip. The average density may be assumed to be 

 equal to that at the middle of the teeth. Ans. About 9 kvv. 



20. Practical Data on Hysteresis Loss. The energy lost in 

 hysteresis per cycle per kilogram of a given material depends only 

 upon the maximum values of B and H, and does not depend upon 

 the manner in which the magnetizing current is varied with the time 

 between its positive and negative maxima. It is only at very high 

 frequencies, such as are used in wireless telegraphy, that the par- 

 ticles of iron do not seem to be able to follow in their grouping the 

 corresponding changes in the exciting current. With such high 

 frequencies iron cores are not only useless, but positively harmful. 

 However, at ordinary commercial frequencies the loss of power 

 Ph due to hysteresis is proportional to the number of cycles per 

 second and can be expressed as 



P h =f-V- F(B) watt., 



where /is the number of magnetic cycles per second, V is the vol- 

 ume of the iron, and F(B) is a function of the maximum flux den- 

 sity B. F(B) represents the loss per cycle per cubic unit of 

 material, and is therefore equal to the area of the hysteresis loop 

 in Fig. 7. 



One can assume empirically that the unit loss per cycle, F(B), 

 increases as a certain power n of B } this power to be determined 

 from tests. The preceding formula becomes then 



...... (20) 



where i) is an empirical coefficient which depends upon the quality 

 of the iron and upon the units used. Dr. Steinmetz found from 

 numerous experiments that the exponent n varies between 1.5 and 

 1.7, and proposed for practical use the formula 



-7 watt, .... (21) 



where the factor 10~ 7 is introduced in order to obtain convenient 

 values for T) when B is in maxwells per square centimeter, and V 

 is in cubic centimeters. It is more convenient for practical calcula- 



