IDEA OF POTENTIAL. 169 



of zero potential. The problem is to determine the electric 

 potential at any given point p at a distance of r centimeters 

 from the center of the sphere, and to do this it is sufficient 

 (according to the statement in Art. 99) to find how much work 

 will be done by the electric field on one coulomb of positive 

 charge which is carried from p to an indefinitely great distance. 

 The path over which the charge is carried is a matter of indiffer- 

 ence; therefore let us choose the straight line ab as the path 

 over which the charge is to be carried. 



The electric field intensity at the element Ax due to the 

 charged sphere is: 



--i 



according to equation (i) of Art. 92, where Q is the amount of 

 charge on the sphere 5. Suppose a body carrying q coulombs 

 is moved along Ax; the force exerted on this body is F = qe, 

 according to Art. 84, or using the above value of e, we have : 



and this force is in the direction of e as shown by the arrow in 

 Fig. 113. Now as the charge q is carried along Ax in the 

 direction of the electric field e an amount of work AW = F-Ax 

 is done by the electric field. Therefore, using the value of F 

 from equation (2), we have: 



and the work W which is done while q is carried from p to 

 infinity is: 



^ 



which gives: 



W = ^- 1 - (5) 



