LENZ'S LAW. 493 



This enunciation defines the conditions in which induced 

 currents are produced. It remains for us to establish the direc- 

 tion and the magnitude. 



511. LENZ'S LAW. A short time after Faraday's discovery, 

 Lenz enunciated the following law, which establishes a connection 

 between the induction produced by the displacement of the inducing 

 system, and the electromagnetic work as defined by Ampere's 

 formula : 



Any displacement of the relative positions of a dosed circuit, and of 

 a current or magnet, develops an induced current, the direction of which 

 is such as would tend to oppose the motion. 



512. NEUMANN'S THEOREM. Lenz's law, which is of great 

 practical utility, merely gives the direction of the induced current, 

 but not the intensity. Assuming, as an experimental fact, that the 

 induction produced in a very short time is proportional to the velocity 

 with which the conductor moves, Neumann has given a complete 

 theory of the induction currents produced in a movable linear 

 conductor in the presence of any magnetic system. He has thus 

 demonstrated this theorem, which we shall afterwards meet with 

 under a more general form : 



The electromotive force of induction is equal to the work which 

 would be done in unit time by the magnetic system, if the intensity of 

 the current in the induced circuit was equal to unity. 



513. THEORY OF HELMHOLTZ AND THOMSON. The existence 

 of phenomena of induction may be considered as a necessary 

 consequence of the conservation of energy combined with the 

 electromagnetic law of Ampere and the law of Joule. This 

 proposition was first put forth in 1847 by Prof. Helmholtz in his 

 celebrated memoir on the Conservation of force. Sir W. Thomson 

 arrived independently at the same conclusions. 



Consider an invariable magnetic system, in the vicinity of a fixed 

 conductor S, in communication with a battery. If the magnet is 

 stationary, the strength I of the permanent current is determined by 

 Ohm's law, and if E is the electromotive force of the battery and R 

 the resistance of the circuit, 



(1) E-I.R. 



Multiplying both sides by I <#, we get 



(2) EI <#= 



