84 STATIC ELECTRICITY 



is proportional to r, and since cross-section X intensity is constant, 

 the intensity is inversely proportional to r, and may be written as 

 \/r. Now if (T is the surface density on the inner cylinder the 

 intensity just outside it is 47r<7, and as this is distant a from the 



*-0 



FIG. 65A. G5B. 



axis we have 47nr = \/a or A = ir<ra. Then between the surfaces 



But 



F- 



E --- 



Integrating, we have 



V = ^Tro-a log r + const 

 and putting V = for the value of V when r = 6, 



V = 4>7ra<r log -. 



If C is the capacity per unit length measured along the axis the 

 area of the inner surface of that length is 2?ra and its charge 



Its potential is 47rflo- log - . Then 



Q 



1 



log^ 21og^ 

 & a a 



Two very long thin equal and parallel cylinders. Let 

 the two cylinders, Fig. 65s, have, each, radius a small compared with 



