235 237] INDUCTION OF CURRENTS. 47 1 



against the positional forces, plus the amount of energy dissipated 

 as heat. For by 70 (5) and (8) 



and therefore 



This theorem was stated by Lord Kelvin in 1860*. 



II. Lenz's Law. In any system of conductors, induced currents 

 due to motion of the conductors are so directed as to oppose the 

 motion. This law, stated by Lenzf in 1834, was, together with 

 Ampere's results, the basis of Neumann's deduction of the laws of 

 induction. 



PARTICULAR CASES OF INDUCTION IN LINEAR CONDUCTORS. 



237. Effect of sudden change of Electromotive Force 

 or Resistance. 



(1) SINGLE CIRCUIT. Let us first consider a single circuit of 

 resistance R Q) containing a constant impressed electromotive 

 force jB"o, and accordingly traversed by the steady current 



Let now the electromotive force or the resistance, or both, be 

 suddenly changed to new values E lt R^. The current now varies 

 from the initial value / , in accordance with the differential 

 equation (5) 235, which becomes 



If we subtract I lt the steady value of the current under the new 

 circumstances, from the total current, the difference 



is called the induced or extra-current. The differential equation 

 thus becomes 



(2) 



whose integral is 



_E 



I (i) =Ae Lt , 



* Nichol's Cyclopaedia, Article " Magnetism, Dynamical Relations of." Reprint 

 of Papers on Electrostatics and Magnetism, 571. 

 t Lenz, Pogg. Ann. 31, p. 439, 1834. 



