28 ON POTENTIAL. 



41. ELECTROSTATIC PRESSURE. Electricity forms, on the surface 

 of a conductor, a very thin layer whose thickness it does not seem 

 possible to determine by experiment, but which is necessarily 

 limited. It is probable that this layer is restricted to the surface 

 of the conductor itself, and that it occupies part of the surrounding 

 dielectrical medium. 



Let A B (Fig. 9) be the thickness of this layer. The force is zero 

 at A on the internal surface S 15 and starting from the point B on the 

 outer surface S 2 , its value is F = 473-0-. In the interval the force varies 

 from to F according to an unknown law. 



Let p be the density at a point M, and V the potential. The 

 force at this point is perpendicular to an equipotential surface which 



dV 



lies between Si and S 2 , and has the value - - . Let e be the 



an 



Fig. 9. 



thickness AB. What has hitherto been called surface density 

 represents the quantity of electricity on the layer e for unit surface ; 

 we have then 



0- = I pdn. 



Let us take three rectangular axes, one of them in the same 

 direction as the perpendicular at M to the equipotential surface, 

 that is the perpendicular to the surfaces S t and So, and the 

 two others of which, x and jy, are in the tangent plane of this 

 equipotential surface. 



7)2y yy 



The second differentials and r r being zero (32), the density 



ox' 2 oy* 



is expressed by, 



