1 82 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



dielectric between the plates. The energy of the charged con- 

 denser is 



W^-^-- x (ii) 



2 ka 



according to equation (65*:). 



Let the battery be disconnected and the plates A and B in- 

 sulated so that q cannot change, and imagine the plates to be 

 pulled apart so as to increase their distance by the amount Ax 

 (the dielectric being a fluid like air or oil). Then the energy of 

 the condenser will be increased by the amount 



This expression for the increase of energy of the charged con- 

 denser is easily derived from equation (ii) by assuming x to in- 

 crease slightly. This increase of energy of the charged condenser 

 comes from the work done in separating the plates against their 

 mutual attraction. Let F be the force of attraction of the plates, 

 then F- kx is the work done against their mutual attraction, and 

 this is equal to bW in equation (iii) so that 



J3 q' 

 ~ 2 ka 

 or 



ka 



(73) 



in which F is the force in joule-units with which two parallel 

 metal plates attract each other, a is the area of each plate in 

 square centimeters, q is the charge on each plate (positive on 

 one, negative on the other) in coulombs, and B is equal to 

 1.131 x io 13 . 



It is noteworthy that the force of attraction is independent of 

 the distance between the plates and inversely proportional to the 

 inductivity of the dielectric, the charge being given. The plates 

 are supposed to be very large in comparison with the distance 

 between them, according to Art. 90. 



