STATIC ELECTRICITY 



If e is the charge per unit length = 



If P is inside the charged surface, the cylinder drawn thr< 

 it now contains no charge, and we see at once that 1 = 



Potential. The description of inverse square system* U MTV 

 much assisted by the use of a quantity termed the potential, which 

 we shall define as follows : 



The potential at a point. If q is an element of charge 

 and r is its distance from the point, the sum of all tin- to in- <y/r, 



36. 



where each element of charge in Ihc system i> <li\i<ll l.\ it- 

 distance from the point, is termed the' potential at the point. 

 The potential is usually denoted by V. \Ye ha\e then V = l///r. 



We shall show that the potential at a point is equal to tin 

 work done in bringing a Mnall body charged with unit quantity 

 from an infinite distance or from outside the field up to the 

 against the forces due to the system. 



Let an element of charge tj be at the point (). I'i^ 

 let the small body with unit charge be moved from a point A b\ 



M 



FIG. 37. 



any path ABC to P. Let B be a point very n. .n to A and let 

 BM be perpendicular to OA. The work done in moving the 



unit from A to B is . AM, since AM is the distance moved 



in the direction of the force. But since AB is very small, we may 

 put AM = OA-OB and OA 2 = OA . OB. 



The work done is therefore q 



q ~ 



