65] 



Charges 



e 



53 



Since C is a point of equilibrium the equipotential through the point C 

 must of course cut itself at C. At C the potential 



4<e e e 

 CA~CB = AB' 



since CA = 2CB. From the loop of this equipotential which surrounds B, 

 the potential must fall continuously to x as we approach .B, since, by the 

 theorem of 51, there can be no maxima or minima of potential between 

 this loop and the point B. Also no equipotential can intersect itself since 

 there are obviously no points of equilibrium except C. One of the inter- 



FIG. 20. 



mediate equipotentials is of special interest, namely that over which the 

 potential is zero. This is the locus of the point P given by 



JL.,_L_O 



PA PB~ 



and is therefore a sphere. This is represented by the outer of the two 

 closed curves which surround B in the figure. 



In the same way we see that the other loop of the equipotential through 

 C must be occupied by equipotentials for which the potential rises steadily 

 to the value + oo at A. So also outside the equipotential through C, the 

 potential falls steadily to the value zero at infinity. Thus the zero equi- 

 potential consists of two spheres the sphere at infinity and the sphere 

 surrounding B which has already been mentioned. 



