CHAPTER VII. 



METHODS FOR THE SOLUTION OF PROBLEMS IN 

 ELECTROSTATICS. 



150. Equipotential Layers as Screens. The theorems 

 of Green, given in 84, have an important electrostatic appli- 

 cation. By the first theorem we may produce at all points outside 

 of a closed surface S the same field as is produced by any electri- 

 fication within S, whose potential is V, by distributing over the 

 surface S a certain surface distribution, and if S is an equipotential 

 surface, the surface density must be 



If now we place on the surface S a distribution whose surface 

 density is cr instead of <r, its effect on outside bodies will be the 

 negative of that of the internal electrifications. Accordingly if a 

 closed equipotential surface completely surrounding electrified 

 bodies be made conducting, we may cover it with such a charge 

 as to completely screen external bodies from the electrical action 

 of the internal charges. By the same theorem the magnitude of 

 the surface charge is equal and opposite to that of the internal 

 electrification. By the theorem for an interior point, we see that 

 upon such an equipotential surface made conducting we may place 

 a charge that shall shield internal points from the action of the 

 external electrifications, the magnitude of the shielding surface 

 charge being now equal to that of the internal charges. 



W. E. 19 



