180 THE MAGNETIC CIRCUIT [ART. 57 



in the design and operation of electrical apparatus and circuits to 

 know the amount of energy stored in the magnetic field, or the 

 electro-magnetic inertia. This inertia modifies the current and 

 voltage relations in the electric circuit in somewhat the same way 

 in which the inertia of the reciprocating parts in an engine modi- 

 fies the useful effort. In mechanical design a revolving part is 

 characterized by its moment of inertia from which the stored 

 energy can be calculated for any desired speed. So in electrical 

 engineering a circuit or an apparatus is characterized by its electro- 

 magnetic inertia or inductance, from which it is possible to calculate 

 the magnetic energy stored in it at any desired value of the cur- 

 rent. In this and in the two next chapters expressions are deduced 

 for the inductance of some of the principal types of apparatus 

 used in electrical engineering. 



Prob. 1. A stationary electromagnet attracts and lifts its armature 

 with a weight attached to it. Explain how the energy necessary for 

 the lifting of the weight is supplied by the electric circuit. 



Prob. 2. A direct-current generator driven by a water-wheel is 

 subjected to very large and sudden fluctuations of the load, which 

 the governor and the gate mechanism are unable to follow properly. 

 A heavy fly-wheel on the generator shaft would improve the operating 

 conditions. Would a reactance coil in series with the main circuit 

 achieve the same result, provided that it could be made large enough 

 to store the required excess of energy ? 



Prob. 3. What experimental evidence could be offered to support 

 the contention that the energy of an electric circuit is contained in the 

 magnetic field linked with the current, and not in the current itself ? 

 The flow of current is usually compared to that of water in a pipe; 

 is not all the kinetic energy stored in the moving water itself and not 

 in the surrounding medium, and if so, is a current of electricity really 

 like a current of water ? 



Prob. 4. Describe in detail current and voltage resonance 1 and 

 free electrical oscillations, from the point of view of the periodic conversion 

 of electromagnetic into electrostatic energy and vice versa, taking account 

 of the dissipation of energy in the resistance of the circuit. 



67. Electromagnetic Energy Expressed through the Linkages 

 of Current and Flux. In order to obtain a general expression for 

 the energy stored in the magnetic field of an electric circuit, con- 

 sider first a single loop of wire aa (Fig. 1 1) through which a steady 

 electric current i is flowing. Let the cross-section of the wire be 

 small as compared to the dimensions of the loop, -so that the flux 



1 See the author's Experimental Electrical Engineering, Vol. 2, pp. 17 to 25. 



