Electrostatics Field of Force 



[CH. ii 



II. Point charges + e, e. 



63. Let charges + e be at the points x a (A, B) respectively. The 

 differential equations of the lines of force are found to be 



dx~X 

 and the integral of this is 



x + a a; a 



= cons. 



The lines of force are shewn in fig. 17. 



FIG. 17. 



III. Electric Doublet. 



64. An important case occurs when we have two large charges -f e, e, 

 equal and opposite in sign, at a small distance apart. Taking Cartesian 

 coordinates, let us suppose we have the charge -I- e at a, 0, and the charge 

 e at - a, 0, 0, so that the distance of the charges is 2a. 



The potential is 



\ f (x of + y* + z* V(a? + a) 2 + y 2 -f z* ' 



and when a is very small, so that squares and higher powers of a may be 

 neglected, this becomes 



If a is made to vanish, while e becomes infinite, in such a way that 

 2ea retains the finite value /j,, the system is described as an electric 



