9 8 



ADVANCED ELECTRICITY AND MAGNETISM. 



the iron when the magnetizing field drops slowly to zero. The 

 work regained is less than the work required to magnetize the iron. 



The work which is lost is repre- 

 sented by the shaded area in Fig. 

 67. 



That area in Fig. 67 represents 

 work may be shown as follows: Ab- 



P 



scissas represent values of 

 scale, so that we may write: 



ax 



or 



Fig. 67. 



Substituting these values of 

 Art. 60 we have 



to 



(i) 

 to 



(2) 



= b-dy 

 and dcB in equation (i) of 



Ordinates represent values of 

 scale, so that we may write: 



$ = by 



W 



abV C 

 = I x 



4* J 



. 



I x-dy 

 - 



(3) 



in which a is the number of units of df represented by one unit 

 of abscissa, and b is the number of units of cB represented by 

 one unit of ordinate in Fig. 67. Now J x-dy is the area between 

 any portion of the cB and $ curve and the y-axis. Therefore, 

 abV/^ir is the nufhber of ergs of work represented by each unit 

 of area between the cB and &C curve and the ^-axis. 



62. Magnetic hysteresis. The magnetic cycle. The diver- 

 gence of the cB and $if curve for increasing values of df from 

 the cB and df curve for decreasing values of d{ is called magnetic 

 hysteresis] or, rather, the tendency of iron to retain a previous 

 magnetic state which is the cause of this divergence is called 

 magnetic hysteresis. One effect of magnetic hysteresis is that 

 the work regained when iron is demagnetized is less than the 

 work which must be spent to magnetize the iron, as pointed out 

 in Art. 61. 



