IDEA OF POTENTIAL. 177 



distant r centimeters from A. Writing x for r in equation 



7? O 

 (i), above, we get - volts per centimeter as the intensity 



.. x 



of the electric field at the element A# in Fig. 1 16, and multiplying 



lines of force 



uipotential surfaces 



zero potential 



line charge 



this by 



Fig. 116. 



we get the volts along Ax, namely: 

 BQ A* 



AE 



27T X 



(2) 



and the total volts between and p is found by integrating 

 this equation from x = I to x = r which gives: 



(3) 



Now the electric field in Fig. 1 16 is directed away from and 

 towards p all along the path, and therefore work is done by the 

 electric field while a positive charge moves from to p, but 

 the potential at p is defined in Art. 99 as the work done by the 

 electric field while one unit of positive charge is transferred from 

 p to 0. Therefore the potential at p in Fig. 1 16 is negative, 

 and from equation (3) we have 

 13 



