EXPRESSION OF ELECTRICAL FORCE AS PRESSURE. 



8 9 



102. The reciprocal action of two systems M l and M 2 is equal to 

 the action of two layers + M^ and M l distributed on the two equi- 

 potential surfaces S x and S 2 , which include M 1 and leave M 2 outside. 



For, consider a second equipotential surface S 2 (Fig. 22) which 

 includes M 15 and again leaves the system M 2 entirely outside. 



Let us arrange a layer + Mj in equilibrium on the surface S 1} and 

 a layer - Mj in equilibrium on S 2 ; the layer on S : may replace the 

 internal system + M^ for all points external to S x ; and the layer on S 2 

 is equivalent to the external system M 2 for all points on the surface S 2 . 



The system of these two layers gives, moreover, a constant 

 potential V 1 -V 2 inside Sj, and a zero potential outside S 2 ; and, 

 finally, a potential varying from Vj V 2 to zero in the intermediate 

 space. The electrical force is therefore everywhere zero, excepting in 

 this space, where it retains the same value at all points, either for the 

 two primitive systems M : and M 2 , or for the equivalent layers 

 distributed on the surfaces S : and S 2 . 



Fig. 22. 



The action of the electrified surface Sj on the layer S 2 is thus the 

 same as on the system M 2 ; that of S 2 , the same on S : as upon M x ; 

 the reciprocal actions of the electrified surfaces S x and S 2 are thus the 

 same as those of the two primitive systems M l and M 2 . 



But we know from the preceding theorems, that the actions ex- 

 perienced by the surfaces Sj and S 2 , are merely the resultants of the 

 electrical pressures /X^i ano - A^2 which are exerted on the elements 

 of these surfaces. If Fj and F 2 are the electrical forces in the medium, 

 the values of these pressures near the elements in question are 



T 



: 8^ 



i 

 8^ 



the first are directed outside the surface S 15 and the second inside 



