ELECTRIC FIELD. 151 



This is the increase of potential energy of the condenser due to 

 the movement Ax, and, as above explained, it is equal to F-Ax. 

 Therefore we have : 



F - Ax = \ - Ax 

 2 ka 



or 



Now, g being in coulombs, equation (3) gives W in joules; 

 so that AW in equation (4) is in joules. Therefore F-Ax is 

 expressed in joules, and F in equation (5) is expressed in joules 

 per centimeter, one joule per centimeter being the force which 

 will do one joule of work while the body on which it acts moves 

 one centimeter in its direction. One joule per centimeter is 

 equal to ten million dynes. 



It is noteworthy that the force of attraction of two parallel 

 charged plates due to given charges + q and q on the plates 

 is independent of the distance between the plates, provided that 

 the plates are very large as compared to the distance between 

 them.* 



The charge q on the two plates is equal to CE, where E 

 is the electromotive force between the plates and C is the 

 capacity of the condenser formed by the two plates. Therefore, 

 substituting the value of C from equation (2), we have: 



I ka ' 



s-j.j-s (6) 



and substituting this value of q in equation (5), we have: 



_!_ kaE? 

 F= 2 B-~ir (7) 



which gives the force of attraction of two plates in terms of the 

 electromotive force between the plates. This equation gives 

 the value of F in joules per centimeter when a is expressed in 



* Equation (2) is true only when * is small as compared with the size of the 

 plates. 



