Examples 65 



17. Three infinite parallel wires cut a plane perpendicular to them in the angular 

 points A, B, C of an equilateral triangle, and have charges e, e, -e' per unit length 

 respectively. Prove that the extreme lines of force which pass from A to C make at 



starting angles ^ n and IT with A C, provided that e' ^> 2e. 



18. A negative point charge e% lies between two positive point charges e and e 3 on 

 the line joining them and at distances a, $ from them respectively. Shew that, if the 

 magnitudes of the charges are given by 



e\ _ 3 _ e%\ 3 , . , 2 



there is a circle at every point of which the force vanishes. Determine the general form 

 of the equipotential surface on which this circle lies. 



19. Charges of electricity <? l5 e 2 , e 3 , (e 3 > e^} are placed in a straight line, the 

 negative charge being midway between the other two. Shew that, if 4e 2 lie between 

 (e 3 *-efy 3 and (e 3 ^ + efy 3 , the number of unit tubes of force that pass from e 1 to e z is 



- s) + = ( - e (e - e + e 



J. 



