ELECTRIC INDUCTION. 293 



22. At the positive surface the magnetic potential is 



F=-g = 2^ ................................ (3). 



At the negative surface 



The normal component of magnetic force at the positive surface is 



dV 



In the case of the magnetic shell, the magnetic force is discontinuous at 

 the surface ; but in the case of the current-sheet this expression gives the value 

 of y within the sheet itself, as well as in the space outside. 



23. Let F, G, H be the components of the electro-magnetic momentum at 

 any point in the sheet, due to external electro-magnetic action as well as to 

 that of the currents in the sheet, then the electromotive force in the direction 

 of x is 



__ 

 ~ dt dx' 



where / is the electric potential* ; and by Ohm's law this is equal to <ru, 

 where cr is the specific resistance of the sheet. 



dF dili 



Hence <ru = -j- -r- 



dt dx 



. ., , 

 Similarly, 



(6) 

 dG " ' 



Let the external system be such that its magnetic potential is represented 

 by v-" , then the actual magnetic potential will be 



(7), 

 and F=^(P. + P), G=- x (P + P), tf=0 ............... (8). 



* "Dynamical Theory of the Electromagnetic Field," Phil. Trans. 1865, p. 483. 



