Impulsive Motion of Electrified Systems. 135 



Putting 1 — ncos 6 = h, we find 



l+n 



w 3fiv?g 2 f fn* — l ± — '2n 2 s\ * aj. k} n 



1— « 



_ 3/^V f J: j^ ^ 4 1 



~ a 3 l3.5 + 5.7r« + 7;^ 4+ "" j ' 



Since the sphere moves along an axis of symmetry, the. 

 momentum carried off by the pulse is given by (38), and 

 thus, after integrating with respect to ~, we have 



p_ ofiucfn C " sin 3 cos 3 6 d6 

 ^ Jo ( 1_ ncosV)' r 



— , • ' r 4 (o — 3« 2 ) log - — 10/i + ., rc d > 

 4aV t. l-« •> J 



_ 6/my f 1 **r 3^ ") 



~ ~ oV 15.7 + 7 . 9t>» + 9 . llr 4 "" J * 



When the sphere is at rest, the electrostatic potential at its 

 surface is Y=gcos 0/Ka 2 , and hence 



i s^tt If 9 cos 6 n a 2 • a 



L o = i%Vq = % ] ^ k^J ■ °b cos 9 . -lira- sm 



d0 



91 _ /4T«r 



2a 3 K~~ ±u? ' 



From these values of W, P, and U we find, by § 15, that 

 for the sphere in steady motion, 



3^y i i w , _3« 4 , ^ G . , I 



i ~ "~ ^ \ 3 . 5 + 5 . 7r + 7 . V)f 4 + y . lie* ^ '" ) 

 ,r^u,f C 1 2a 2 3^ , A* "> 



