30 ELECTRICAL ENGINEERING 



and the energy stored per cubic centimeter is 



These two equations represent the potential energy of the field. 

 Stresses exist throughout the field tending to reduce the potential 

 energy to a minimum; first, there is a tension along the lines of 

 induction tending to shorten them and to draw the bounding 

 surfaces of the field together and so reduce the volume to zero; 

 second, there is a pressure at right angles to the lines tending 

 to spread them apart and so reduce the density in the field. 

 Since the system is in equilibrium these two stresses are of equal 

 magnitude. 



To obtain an expression for the stress per square centimeter on 

 the bounding surfaces, consider the parallel plate condenser in 

 Fig. 23. The energy stored in the field is by equation 55 



If a force of P dynes is applied to one of the plates and the dis- 

 tance between the plates is increased by amount dt, the work done 

 is P dt ergs. The charges on the plates are assumed to remain 

 constant and therefore the flux density remains constant, but 

 the volume of the field is increased by the amount A dt cu. cm., 



S) 2 



and the energy stored in it is increased by A dt X o~iF> DU ^ the 



O TTli. 



increase in the stored energy is equal to the work done by the 

 force P and, therefore, 



and 



..... (59) 



This is the pull exerted by the field on each plate of the condenser 

 tending to draw them together. 

 The pull per square centimeter is 



thus, the pull per square centimeter on any charged surface is 

 equal to the square of the induction density at the point divided 

 bySirK. 



