Electrostatics Field of Force 



[CH. ii 



V. Three equal charges at the corners of an equilateral triangle. 



66. As a further example we may examine the disposition of equi- 

 potentials when the field is produced by three point charges at the comers 

 of an equilateral triangle. The intersection of these by the plane in which 

 the charges lie is represented in fig. 21, in which A, B, C are the points at 

 which the charges are placed, and D is the centre of the triangle ABC. 



It will be found that there are three points of equilibrium, one on each 

 of the lines AD, BD, CD. Taking AD = a, the distance of each point of 

 equilibrium from D is just less than Ja. The same equipotential passes 

 through all three points of equilibrium. If the charge at each of the points 



A, B, C is taken to be unity, this equipotential has a potential - . 



a 



The 



FIG. 21. 



equipotential has three loops surrounding the points A, B, C. In each of 

 these loops the equipotentials are closed curves, which finally reduce to 

 small circles surrounding the points A, B, C. Those drawn correspond to 

 3'25 3'5 375 

 a 



304 



.-, . . . T O A3 O O O i O 



the potentials - , , - 



and -. 



a 



Outside the equipotential 



the equipotentials are closed curves 



