ELECTROSTATICS 29 



The potential difference between the plates is 



E = m = -p, 



j\. 



and the capacity of the condenser by equation 37 is 



AK 



~~^i 



Substituting these values for E and C in equation 52 gives a 

 fourth expression for the energy stored in the field, namely 



(55) 



Since the volume of the field is At cubic centimeters and the flux 

 density is uniform, the energy stored per cubic centimeter of the 

 field is 



or 



(57) 



Thus, the energy stored per cubic centimeter in an electro- 

 static field is equal to the square of the dielectric flux density 



multiplied by 5 ^ , or is equal to the square of the intensity of 



O 7TA 



rr 



the electrostatic force multiplied by ^ . 



O 7T 



From equation 52 a very useful definition of capacity may be 

 obtained, 



r 2W 



~2> ....... 



or the capacity of a condenser is equal to twice the energy stored 

 in its field divided by the square of the difference of potential 

 across its terminals, or the capacity is equal to twice the energy 

 stored when the difference of potential is unity. 



25. Stresses in an Electrostatic Field. The -energy stored in an 

 electrostatic field is 



72 



W = C 



