150 ADVANCED ELECTRICITY AND MAGNETISM. 



way, the total voltage between the wire and the outside metal 

 sheath is subdivided into equal parts in the various layers of 

 insulating material. 



90. Attraction of parallel charged plates. Two parallel metal 

 plates each a square centimeters in area are placed at a distance 

 of x centimeters apart in an insulating fluid, such as air or oil, 

 of which the inductivity is k. The charge on one plate is +2 

 coulombs and the charge on the other plate is q coulombs, 

 and these charges remain constant, because the battery is dis- 

 connected and the plates are insulated. Let F be the force 

 with which the p'ates attract each other; then, if the plates be 

 moved farther apart so that x is increased to x + Ax, an amount 

 of work equal to F-Ax will be done, and this work will all go to 

 increase the energy of the charged condenser; therefore if we 

 can calculate the increase of' the potential energy of the con- 

 denser due to the movement A#, we will arrive at an expression 

 for the force F. 



The energy of a charged condenser, expressed in terms of its 

 capacity C and charge g, is given by equation (6) of Art. 81, 



namely : * n z 



TF=|| (i) 



and the capacity of a parallel-plate condenser is: 



'-S-T W 



as explained in Art. 79. Therefore, substituting this value of 

 C in equation (i) we have: 



*- ( 3 ) 



Differentiating this expression with respect to x, we have: 



* is written for the constant G of Art. 79 so that the value of B is 



D 



1.131 X io*. 



