Dielectric  Strength  of  Air,  259 
10.    The  Maximum  Electric  Intensity  between  a  Sphere 
and  a  Plane. 
When  the  plane  is  at  zero  potential,  we  see,  by  taking  the 
image  of  the  sphere  in  the  plane,  that 
H«=0W/»      .....     (26) 
where  fp  is  the  value  of  the  factor  /  given  above  correspond- 
ing to  2x/a  ;  os  being  the  least  distance  of  a  point  on  the 
sphere  from  the  plane  and  a  being  its  radius. 
11.   The  Maximum  Electric  Intensity  between  two  infinitely 
long  parallel  Cylinders. 
Let  us  consider  the  value  of  the  electric  potential  at  points 
between  the  two  cylinders,  the  sections  of  which  by  the 
plane  of  the   paper  are  shown  in  fig.  3.     If  g  and  —  q  be  the 
Kff,  3. 
rC~D  =  d=the  distance  between  the  axes  of  the  two  parallel  cylinders. 
LM=,r  =  the  minimum  distance  between  the  cylinders. 
«=the  radius  of  either  cylinder. 
A  and  B  are  inverse  points.         CA  .  CB  =  CL2=DA  .  DB. 
charges  per  unit  length  on  the  cylinders  the  axes  of  which 
pass  through  A  and  D  respectively,  the  potential  v  at  any 
point  P  external  to  them  is  given  by 
v=-2?lojg(AP/BP), 
where  A  and  B  are  the  inverse  points  of  the  circular  sections. 
The  maximum  values  Hm  of  the  electric  intensity  will  be  at 
L  and  M.     The  potential  at  any  point  p  on  CD  will  be 
v=—2q log r  +  2g  log  (c  —  r) , 
where  r  is  Ap  and  c  is  the  distance  AB.     Hence 
r       c  —  r 
S  2 
