CHAPTER XII 



INDUCTION OF CURRENTS. 



235. Systems of Currents as Cyclic Systems. The 



phenomena of the induction of electric currents by changes in 

 the magnetic field were discovered by Faraday in 1831*. The 

 results obtained experimentally by Faraday were deduced mathe- 

 matically from the law of Lenz (see below), and from Ampere's 

 results regarding magnetic shells, together with the principle of 

 Conservation of Energy by F. E. Neumann f in 1845. The credit 

 is due to Max well J of having had the idea of treating a system of 

 currents and the magnetic field belonging to them as a mechanical 

 system, subject to the ordinary laws of motion, and of thus de- 

 ducing the equations of induction from the generalized equations 

 of Lagrange and Hamilton. The particular class of systems to 

 which currents may be assimilated is that studied by Helmholtz 

 under the name of cyclic systems, a detailed treatment of which 

 has been given in Chapter III. 



We have seen in the last chapter that if the strengths of a 

 system of currents be maintained constant, the currents tend to 

 move in such a way that the energy of the field produced by them 

 tends to increase. This energy is a homogeneous quadratic function 

 of the strengths of the various currents, the coefficients, which we 

 have called inductances, being determined by the form and rela- 

 tive position of the circuits, and the nature of the medium in 

 which they are situated. The medium being specified, these 

 geometrical specifications of the circuits may be made by giving 



* Faraday, Experimental Researches in Electricity, Vol. i. p. 1. 



t F. E. Neumann, " Ailgemeine Gesetze der inducirten Strome," Abh. Berl. 

 Akad., 1845. 



J Maxwell, "A Dynamical Theory of the Electromagnetic Field," Phil. Trans. 

 CLV. 1864. Sci. Papers, Vol. i. p. 526. 



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