CONDUCTING SPHERE IN A UNIFORM FIELD. 143 



To obtain the electrical state of a conducting sphere in a uniform 

 field of strength </>, F^ may be replaced by - < in all the preceding 

 formulae, which gives 



(f>r cos W, 



a 3 

 < cosw, 



</> 3 sin to cos w, 



- 



160. If R be the radius of the circle, drawn on an equipotential 

 surface, through which would pass the same flow in the original 

 field that is to say, of the circle which comprises all the lines 

 of force directed towards the conducting sphere we have 



This circle has therefore a surface three times as great as a great 

 circle of the sphere. 



All the lines of force terminate perpendicularly at the surface 

 of the sphere and proceed perpendicularly from it, always excepting 

 those which fall upon the equator ; these make with the normal an 

 angle of 45. 



