38 THE MAGNETIC CIRCUIT [ART. 16 



16. The Loss of Energy per Cycle of Magnetization. When a 

 magnetic flux is maintained constant the only energy supplied 

 from the source of electric power is that converted into the i 2 r 

 heat in the exciting winding; no energy is necessary to maintain 

 the magnetic flux. This is an experimental fact, fundamental in 

 the theory of magnetic phenomena. When, however, the flux 

 is made to vary, by varying the exciting ampere-turns or the 

 reluctance of the magnetic circuit, electromotive forces are 

 induced in the magnetizing, winding by the changing flux. 

 A transfer of energy results between the electric and the magnetic 

 circuits. 



Beginning, for instance, at the point A of the cycle (Fig. 7), 

 and going toward C, the flux is forced to decrease. According A 

 to Faraday's law, the e.m.f. induced'by this ^ux in the magnetix- 



ing winding is such as to resist the change, i.e., it tends to main- 

 tain the current. Therefore, during the part AC of the cycle 

 energy is supplied from the magnetic to the electric circuit. 

 This shows that energy is stored in a magnetic field. During the 

 part CFA' of the hysteresis loop energy is supplied from the 

 electric to the magnetic circuit, because at the point C, the 

 current is reversed and becomes opposed to the e.m.f. The 

 other half of the cycle being symmetrical, with the flux and the 

 current reversed, energy is returned to the electric circuit during 

 the part A'C' of the cycle, and is again accumulated in the 

 magnetic circuit during the part C'F'A . 



If the part AC of the cycle were identical with C'F'A, and the 

 part A'C' were identical with CFA', the amounts of energy trans- 

 ferred both ways would be the same, and there would be no net 

 loss of energy at the end of the cycle. In reality the two parts 

 are different; the amounts of energy returned from the magnetic 

 circuit to the electric circuit in the parts AC and A'C' are smaller 

 than the amounts supplied by the electric circuit in the parts 

 CFA' and C'F'A. This is because the last two parts of the curve 

 are more steep than the first two, and consequently the induced 

 e.m.fs. are larger for the same values of the current. The net 

 result is therefore an input of energy from the electric into the 

 magnetic circuit, this energy being converted into heat in the iron. 

 No such effect is observed with non-magnetic materials, because 

 the two branches of a complete B-H cycle coincide with a straight 

 line passing through the origin. 



