142 PARTICULAR CASES OF EQUILIBRIUM. 



maximum density S , or of the internal force F^ ; if a be the radius 

 of the sphere and u its volume, we have 





# _ # 3 _ 3 cos w 



V. = wo- = - F, x = - F; - 



6 U o to * o 





ft 

 Y e = ~Y 3 sin w cos w = - F { 3 sm w cos w, 



2 coso>= -2^ cosw, 



. 



^smo>= -F { sinw, 



o = _ F 2 

 4 a 4 



159. CONDUCTING SPHERE IN A UNIFORM FIELD. Suppose 

 now that a sphere thus electrified is placed in a uniform field, of 

 strength <f>, parallel to the axis of x, and let V be the value of the 

 potential in the plane which passes through the centre. If we have 



the resultant force is null in the whole sphere; the potential is 

 therefore constant, and there is equilibrium if the sphere is a con- 

 ductor. 



