40 THE MAGNETIC CIRCUIT [ART. 17 



(19) represents the area of the figure ACQ, which is therefore a 

 measure for the energy transferred to the electric circuit, per cubic 

 centimeter. In exactly the same way it can be shown that the 

 energy supplied to the magnetic circuit during the part C'A of the 

 cycle is represented by the area AC'Q. Hence the net energy 

 loss for the part of the cycle to the right of the axis of ordinates 

 is represented by the area ACC'A. Repeating the same reasoning 

 for the left-hand side of the loop it will be seen that the total 

 energy loss per cycle of magnetization per cubic centimeter of 

 material is represented by the area AC A' C'A of the hysteresis 

 loop. For a given material, this area, and consequently the loss, 

 is a function of the maximum flux density PA, and increases with 

 it according to a rather complicated law. Two empirical formulae 

 for the loss of energy as a function of the density are given in Art. 

 20 below. 



In the problems that follow the weight of one cubic decimeter 

 of solid carbon steel is taken to be 7.8 kg., and that of the alloyed 

 or silicon steel 7.5 kg. The weight of one cubic decimeter of 

 assembled carbon steel laminations is taken as 0.9X7.8 = 7 kg., 

 and that of silicon steel laminations as 0.9X7. 5 = about 6.8 kg. 



Prob. 6. A hysteresis loop is plotted to the following scales : abscissa? 

 1 cm. = 10 amp .-turns /cm. ; ordinates, 1 cm. = 1 kilo-maxwell /sq. cm. ; the 

 area of the loop is found by a planimeter to be 72 sq. cm. What is the 

 loss per cycle per cubic decimeter of iron? 



Ans. 7. 2 watt-seconds (joules). 



Prob. 6. The hysteresis loop mentioned in the preceding problem was 

 obtained from an oscillographic record at a frequency of 60 cy., with a sam- 

 ple of iron which weighed 9.2 kg. What was the power lost in hysteresis 

 in the whole ring? Ans. 510 watts. 



Prob. 7. The stationary coil of a ballistic electro-dynamometer is con- 

 nected in series with the exciting electric circuit (Fig. 1) ; the moving coil 

 is connected through a high resistance to a secondary winding placed on 

 the ring. The exciting current is brought to a certain value, and then the 

 current is reversed twice in rapid succession, in order that the iron may 

 undergo a complete magnetization cycle. Show that the deflection of the 

 electro-dynamometer is a measure for the area of the hysteresis loop. 

 Hint: HdB=H(dB/dt) <ft=Const. X iedt. 1 



17. Eddy Currents in Iron. Iron is an electrical conductor; 

 therefore when a magnetic flux varies in it, electric currents are 



Dearie, "The Ballistic Measurement of Hysteresis," Electrician, Vol. 

 49, 1902, p. 100. 



