496 INDUCTION. 



We get from this, by a reasoning analogous to that which gave 

 equation (8), 



Whatever be the law by which the magnetic system is displaced, 

 if the strength of the currents is the same at the two limits, the last 

 term of equation (8') is null. This is the case more particularly 

 if the limits are chosen before and after the motion, in which case 

 the two limiting values of the current are equal to I . 



With these limitations we may enunciate in a general form the 

 theorem expressed by equation (8) : 



The total quantity of electricity put in motion by any displacement of 

 a magnetic system, is equal to the quotient of the variation of the flow of 

 force corresponding to this displacement, by the resistance of the circuit. 



517. The preceding results suggest some important remarks. 



i st. It is seen, in the first place, that the electromotive force of 

 induction is of a kind which opposes the motion, for the original 

 intensity of the current is diminished or increased according as the 

 magnetic system obeys or resists electromagnetic actions ; this is 

 Lenz's law. 



2nd. If the strength of the current were equal to unity, the 



external work dT would correspond to the work in unit time. 



The electromotive force of induction is equal to this work ; this 

 is Neumanris theorem. 



3rd. The electromotive force of induction is independent of the 

 electromotive force E of the battery ; the induction is then the same 

 however feeble is the strength of the original current. It results 

 from this, that induction should also take place when the conductor 

 is neutral, provided it forms a closed circuit. It is in this form that 

 Faraday discovered induction currents. 



It must, however, be observed that if the current was really null 

 throughout the entire extent of the conductor, the reciprocal action 

 of the magnet and of the circuit would also be null, and the 

 preceding considerations would not enable us to foresee the pro- 

 duction of induced currents. But it may be said that this perfect 

 neutrality is a state of unstable equilibrium, impossible to realise in 

 practice, and that an infinitely slight cause, a change of temperature 

 at any point of the circuit, or the displacement of an external 

 electrified body, even at a great distance, would be sufficient to 

 produce a current, however slight, in the conductor, and thus enable 

 induction to take place. 



