CHAP. Ill] HYSTERESIS AND EDDY CURRENTS 37 



external force is entirely removed, the body is still somewhat to 

 the right of its central position, because the friction balances part 

 of the tension of the springs. Here we have something analogous 

 to residual magnetism and to the part AC of the hysteresis loop. 

 A finite force H is required in the negative direction to bring Q 

 to the center. This force corresponds to the coercive force of a 

 piece of iron. 



By following this analog)' through the complete cycle one 

 can show that a loop is obtained similar to a hysteresis loop. 

 Also, it can be shown that the phenomenon is irreversible, and 

 that total work done by the force H is equal to the work of friction. 

 Moreover there is a periodic interchange of energy between the 

 springs and the source of the force //, and the net loss of energy 

 is represented by the area of the loop corresponding to Fig. 7. 



Prob. 1. An iron ring is thoroughly demagnetized, and then the cur- 

 rent in the exciting winding is varied in the following manner: It is 

 increased gradually from zero to 1 ampere and is then reduced to zero. 

 After this, the current is increased to 2 amperes in the same direction, and 

 again reduced to zero. Then the current is increased to 3 amperes again in 

 the same direction, and reduced to zero, etc. Draw roughly the general 

 character of the B-H curve, taking the hysteresis into consideration. 

 Hint : First study a similar process on the mechanical analogy shown in 

 S. 



Prob. 2. A piece of iron is made to undergo a magnetization process 

 from the point A (Fig. 7) to a point between F and A' such that, when 

 subsequently the exciting circuit is opened, the ascending branch of the 

 hysteresis curve comes to the origin. Show that such a process does not 

 bring the iron into the neutral virgin state, in spite of the fact that B-0 

 for //-O. Hint : Consider the further behavior of the iron for positive 

 an<i IM lues of //. 



Prob. 3. A millivolt meter is connected to the high-tension terminals 

 of a transformer, and the current in the low-tension winding is varied in 

 -I- h a way as to keep the voltage constant: Show that the curve of the 

 current plotted against time is proportional to the hysteresis loop of tho 

 core. Hint : Since d0/dt is constant, is proportional to the time. 



Prob. 4. The magnetic flux density in an iron core is to vary with the 

 time according to the sine law. Plot to time as abscissa* the instantane- 

 ous values of the exciting ampere-turns per centimeter length of th< 

 from an available hysteresis loop, and show that the wave of the exciting 

 current is not a sine wave and is unsymmetrical. Note: This problem 

 has an appli. -at ion in the calculation of the exciting current of a trans- 

 former; see Art. 33 below. 



1 A solution of thin and of the next problem will be found in Chapter V 

 of Ewing'a Magnetic Induction in Iron and other MctaU, 1802. 



