52 



Electrostatics Field of Force 



[CH. II 



IV. Point charges +4e, e. 



65. Fig. 19 represents the distribution of the lines of force when the 

 electric field is produced by two point charges, 4- 4e at A and e at B. 



At infinity the resultant force will be 3e/r 2 , where r is the distance from 

 a point near to A and B. The direction of this force is outwards. Thus no 

 lines of force can arrive at B from infinity, so that all the lines of force 

 which enter B must come from A. The remaining lines of force from A go 

 to infinity. The tubes of force from A to B form a bundle of aggregate 



FIG. 19. 



strength e, while those from A to infinity have aggregate strength 30. The 

 two bundles of tubes of force are separated by the lines of force through C. 

 At G the direction of the resultant force is clearly indeterminate, so that G 

 is a point of equilibrium. As the condition that G is a point of equilibrium 



we have 



4ie e 



BC'< 



= 0. 



So that AB = BC. At C the two lines of force from A coalesce and then 

 separate out into two distinct lines of force, one from G to B, and the other 

 from G to infinity in the direction opposite to CB. 



The equipotentials in this field, the system of curves 



4 1 



pZ = p5 = cons " 



are represented in fig. 20, which is drawn on the same scale as fig. 19. 



