58 THE MAGNETIC CIRCUIT [ART. 24 



transformer action d$ can also be considered as the flux which cuts 

 the loop during the time dt, the same as in the generator action. 

 On the other hand, the moving conductor in a generator is a part 

 of a turn of wire, and any flux which it cuts either increases or 

 decreases the total flux linking with the loop. Consequently, in the 

 case of the generator action d<D can be interpreted as the change of 

 ilux within the loop, the same as in the transformer action. Thus, 

 the mathematical expression for the induced e.m.f. is the same 

 in both cases, provided that the proper interpretation is given to 

 the value of dd>. 



The sign minus in formula (25) is understood with reference to 

 the right-hand screw rule (Art. 1), i.e., with reference to the direc- 

 tion of the current which would flow as a result of the induced 

 electromotive force. Namely, the law of the conservation of 

 energy requires that this induced current must oppose any change 

 in the flux linking with the secondary circuit. If this were other- 

 wise, a slight increase in the flux would result in a further indefinite 

 increase in the flux, and any slight motion of a conductor across a 

 magnetic field would help further motion. 



The positive direction of the induced e.m.f. is understood to be 

 that of the primary current which excites the flux at the moment 

 under consideration. If the flux linked with the secondary circuit 

 increases, d<D/dt in formula (25) is positive, but the secondary 

 current must be opposite to the primary in order to oppose the 

 increase. Thus, the secondary current is negative, and by assump- 

 tion the induced e.m.f. e is also negative. Therefore, the sign 

 minus is necessary in the formula. When the flux decreases, 

 d/dt is negative, but the secondary current is positive, because it 

 must oppose the reduction in flux. Hence, in order to make e a 

 positive quantity, the sign minus is again necessary. 



The following two special cases of formula (25) are convenient 

 in applications. Formula (25) gives the instantaneous value of 

 the induced e.m.f.; it is once and a while required to know the 

 average e.m.f. induced during a finite change of the flux from 4>i 

 to 4> 2 . By definition, the average e.m.f. is 



eave=-. T- i edt, 



l2 tiJ tl 



where ti is the initial moment and t 2 the final moment of the 

 interval of time during which the change in the flux takes place. 



