IDEA OF POTENTIAL. 183 



dV 

 then -j = e, so that V = ex + a constant. Therefore if we 



choose the ^-axis as the region of zero potential we must have 

 V = o when x = o. Therefore the constant of integration is 

 zero, and we have: 



V = ex (i) 



where V is the potential at any point whose abscissa is x. 



Potential due to a line doublet. Consider two equal and opposite 

 line charges parallel to each other and at a distance Ax apart, 

 let + Q and Q be the charges per centimeter, and let the 

 product Q-Ax be a finite quantity M. Such a pair of infini- 

 tesimally distant, equal and opposite line charges is called a 

 line doublet, and M is called the moment of the doublet. 



The potential at a point due to a line doublet is found as 

 follows: The potential at the point p in Fig. 124 due to the line 



-Q 



Fig. 124. 

 The distance r is supposed to be very large in comparison with A*. 



charge + Q is log e r, and the potential at p due to 



73D 

 the line charge - Q is + log e (r + Ar), according to 



equation (4) of Art. 106. Therefore the net potential at p 

 due to both line charges is: 



[log. (r + Ar) - log. r] = - d (log. r) = . I . dr 



