MEASUREMENT OF PERMEABILITY 



277 



The left-hand side, CEefa, is the energy supplied to the coil by 

 the external source of current in time dt. C*Rdt is the energy 

 dissipated as heat in the wire according to Joule^s law. Then 

 ?iaCdB is the energy supplied to the iron in increasing the 

 induction by dB. 



If / is the mean length of the iron its volume is /a, so that the 



,. , . 7iCdB 



energy supplied to unit volume is - . 



If H is the intensity of the field within the coil, H/ = 47rnC, 



., . nC H 

 so that = - . 



/ 4-7T 



Hence the energy supplied per unit volume in the increase of 

 magnetic induction dB is 



HdB 



47T " 



Let CD, Fig. 212, represent the hysteresis loop when the 

 curve is drawn with abscissa representing H and ordinate repre- 

 senting B. Let PQ be an element in the ascending branch. The 



PQNM 

 strip PQNM is H//B, so that the energy supplied is 



47T 



In 



the descending branch there will be an element Q'P', with both H 



B 



s' 



/ 



Fia. 212. 



and dB negative, so that HdB will be positive and the energy 



supplied there is + 



FQ'NM 



The total for the two elements is 

 PQQT 



47T ' 



For an element RS higher up the curve on the ascending 

 branch and for the corresponding element R'S' on the descending 



