CHAPTER X 

 ELECTROMAGNETIC ENERGY AND INDUCTANCE 



56. The Energy Stored in an Electromagnetic Field. Experi- 

 ment shows that no supply of energy is required to maintain a 

 constant magnetic field. The power input into the exciting coil or 

 coils is in this case exactly equal to that converted into the i?r heat 

 in the conductors, and this power is the same whether a magnetic 

 field is produced or not. Another familiar example is that of a 

 permanent magnet, which maintains a magnetic field without any 

 supply of energy from the outside, and apparently without any 

 decrease in its internal energy. Nevertheless, every magnetic field 

 has a certain amount of energy stored within it, though in a form 

 yet unknown. This is proved by the fact that an expenditure of 

 energy is required to increase the field, and, on the other hand, 

 when the flux is reduced, some energy is returned into the 

 CM it ing electric circuit. 



The conversion of electric into magnetic energy and vice 

 versa is accomplished through the e.m.f. induced by the vary- 

 ing flux. Let a magnetic flux be excited by a coil CC (Fijr. !">> 

 supplied with current from a source of constant voltage E, and let 

 he u rheostat r in series with the coil. Let part of the resist- 

 ance in the rheostat be suddenly cut out in order to increase the 

 current in the coil. It will be found that the current rises to its 

 final value not instantly; namely, when the current increases, the 

 flux also increases, and in so doing it induces in the electric circuit 

 an e.m.f., say e, which tends to oppose the current. This e, 

 together with the ilt drop, balances the voltage E, so that for a 

 t ime the power Ei supplied by the source is larger than the power 

 -'/' lst in the total resistance of the circuit. The difference, 

 Eii?/t, is stored in the magnetic field created by the coil and l.y 

 her parts of the circuit. Tl v eidt supplied by the 



electric circuit during the Heinent of time (It is eon verted into the 

 magn- u'y of the field, by the law of the conservation of 



177 



