ELEMENTARY THEORY OF ELECTROMAGNETISM. 43 



determined by connecting a voltmeter between the brushes of 

 the dynamo and taking the reading of the voltmeter, provided 

 the dynamo brushes are properly located and provided there is 

 but very little current flowing through the armature. When a 

 considerable current is flowing through the armature a portion 

 of the total induced electromotive force is lost in overcoming the 

 resistance of the armature windings. 



29. Expression of induced elect omotive force in terms of the 

 rate of change of the magne.ic flux which passes through a 

 circuit. Figure 31 shows a wire be sliding sidewise at a velocity 

 of v centimeters per second along two rails. The electromotive 

 force induced in the moving wire is Hlv according to Art. 24, 

 and this electromotive force acts to produce current in the circuit 

 abed; the intensity of the magnetic field in Fig. 31 being H 

 gausses at right angles to the plane of the paper. 



The area of abed is Ix square centimeters, and the magnetic 

 flux <I> which passes through the opening abed is found by 

 multiplying H by the area Ix; that is: 



* = Hlx (i) 



Now if x changes, < must change HI times as fast, that is: 



dx 

 dt 

 Therefore equation (2) becomes : 



But, -j- is the velocity v at which the wire moves sidewise. 



Tt= Hk k) 



Therefore, remembering that Hlv is the electromotive force 

 induced in be, and remembering that < is the magnetic flux 

 through the opening abed, we have the following proposition: 

 When the magnetic flux $ through the opening of a circuit 

 changes, an electromotive force is induced in the circuit, and 



