MAGNETISM AND ELECTROMAGNETICS 



73 



force is oc; this force is called the coercive force. If the current 

 is still increased until it reaches its maximum value / again, the 

 induction density will have the same maximum value as before. 

 If the cycle is completed by again reducing and reversing the 

 current the closed curve arca^da shows the relation between $ 

 and 3C. This closed curve is called a hysteresis loop. 



FIG. 61. Hysteresis loop. 



The area of the hysteresis loop represents a loss of energy since, 

 from Art. 47, the work done in increasing the flux threading the 

 solenoid by amount d$ is 



ni , 



where n is the number of turns on the coil and i is the current 

 in amperes flowing when the flux threading the coil is <. If the 

 ring has a constant section A sq. cm. and length I cm. then, since 



A *rr f Y) f ) 



and d<f> = A dB, the work done is 



<fa = Wd>, (107) 



SIC = 



10 1 



