3 86 



Note i 2 : electric capacity 



distance b from any one of the generating lines of the cylinder, and therefore 

 the potential at any point on the axis is the same as if the whole charge had 

 been collected on one generating line. 



Hence at the point on the axis for which x = , if we write 



L = log-^ v - + log- T - , (24) 



the potential due to the distribution whose linear density is 



is 



" " "WL 2.2 2.3.3 2.3.4.4 



approximately, provided is between I. 

 Thus, if A,, = A , 



Al = y4l 7' 



* 2 _ *\ 



(27) 



/3<5 x* is x 2 3\ 



1 A I *J+J +J i _* \ 



4 ~~~ ^^ 4 I O 74 i 72 ' O / > 



\ o fr 4 i o/ 



then iji = ^4 Z-, 



I- 2), 



? I\ ,r ,s 



L ~ 3)> (28) 



I5| 2 + 3\ (_2B) 



These values of the potential are calculated for the axis of the cyb'nder. 

 The potential at the curved surface may be found from that at the axis by 

 remembering that within the cylinder V 2 ^ = o. At a distance b from the axis 

 the potential is therefore 



, i i d^ us i d^ w 



w, = w is b -f- 2. ~+K O utC.i (2Q) 



where the values of t/j and its derivatives are those at the axis. 

 For a uniform distribution 



d 2 Ji . (I I + A 



jf* = ~ A O( JT + -JT) (3) 



which is approximately - p , when = o, and j , when = I. Hence, 



I 2/ 



when the length of the cylinder is many times its diameter, the potential at 





