ELEMENTARY THEORY OF ELECTROMAGNETISM. 53 



, the pull of the mule must 

 at 



dl 

 exceed RI by an amount L 



as stated above, and the boat 

 pulls back on the mule with a 

 force which exceeds RI by an 



amount L^-. This additional 

 at 



backward pull of the boat on 

 the mule \Ljl J is called the 

 inertia reaction of the boat. 



dl 



the rate 37, the propelling 

 at 



electromotive force must ex- 



ceed 



dl 



RI by an amount L jr 



as stated above, because the 

 propelling electromotive force 

 must overcome not only the 

 resistance reaction RI of the 

 circuit, but it must also over- 

 come the self-induced electro- 

 motive force due to the in- 

 creasing current. 



Self -induced electromotive force in a circuit is exactly analo- 

 gous to the inertia reaction of a boat. 



35. Kinetic energy of a current in a circuit. 



Work done on a body which 

 moves without friction would 

 all go to increase the kinetic 

 energy stored in the body. 



If W is the amount of ki- 

 netic energy stored in a body, 



dW . 



then -3 (the rate of increase 

 at 



of W) is the rate at which work 

 is done on the body to cause its 

 speed to increase. 



The rate at which work is 

 done by a propelling force E 

 is El, where I is the velocity 

 of the body. Therefore, using 

 the value of E from equation 

 (i) of Art. 33, and remember- 

 ing that the rate at which work 



Work done on a circuit which 

 has zero resistance would all go 

 to increase the kinetic energy 

 stored in the circuit. 



If W is the amount of ki- 

 netic energy stored in a circuit, 



dW . 

 then r- (the rate of increase 



of W) is the rate at which work 

 is done on the circuit to cause 

 the current to increase. 



The rate at which work is 

 done by a "propelling'* electro- 

 motive force E is El, where 

 / is the current flowing in the 

 circuit. Therefore, using the 

 value of E from equation .(2) 

 of Art. 33, and remembering 



