CHAPTER V. 



INDUCED ELECTROMOTIVE FORCE. 



THE DYNAMO. 



62. Leaz'slaw. Electromagnetic theory a branch of mechanics.* 

 The idea of electric current is strictly analogous to the mechan- 

 ical idea of velocity f and an insight into the nature of induced 

 electromotive force can be obtained only by drawing a parallel 

 between the equations in Mechanics and the equations of Elec- 

 tricity and Magnetism. 



The product of the force F exerted on 

 a body which moves at velocity v in the 

 direction of F is equal to the power P 

 developed by the agent which is exerting 

 the force on the body ; that 'is 



The product of the electromotive force 

 E of a generator and the current / de- 

 livered by the generator is equal to the 

 power P delivered by the generator to 

 the circuit to which the generator delivers 

 current. That is, 



P=ES 



in which P is expressed in ergs per sec- 

 ond if E is expressed in abvolts and 1 

 in abamperes, or P is expressed in watts 

 if E is expressed in volts and / in 

 amperes. 



In order to produce a current / through 

 a circuit of which the resistance is R, an 

 electromotive force equal to RI is re- 

 quired ; that is, 



E = RI 



Multiplying both members of this equation 



P=Fv 



in which P is expressed in ergs per sec- 

 ond if F is expressed in dynes and v in 

 centimeters per second. There are no 

 names for the units of force and velocity 

 which correspond to the watt as a unit 

 of power. 



A force F acts upon a boat and in- 

 creases the velocity v of the boat until 

 all of the force F is used to overcome the 

 friction of the water. Let us assume that 

 the friction of the water is proportional 

 to the velocity of the boat, or equal to rv 



* The mechanical analogies which are outlined in this article are exact and com- 

 plete. Any one who is interested in the full details of this matter should read a re- 

 markable paper on The Motion of Monocyclic Systems by H. von Helmholtz, Crelle's 

 Journal, Vol. 97, pp. in and 317. A very interesting and instructive book entitled 

 Applications of Dynamics to Physics and Chemistry, by J. J. Thomson, touches in- 

 directly upon this matter. See also Art. 125 of this text. 



t Electric current is velocity and it is entirely meaningless to speak of the 

 velocity with which an electric current flows along a wire. This matter will be made 

 clear when we come to discuss electric waves. 



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