84 Conductors and Condensers [OH. in 



distance of the plates being d, so that C = A/4>Trd, by 83. Let a be the 

 surface density of the high potential plate, so that e = <rA. Let the low 

 potential plate be at zero potential, then the potential of the high potential 

 plate is 



and the electrical energy is 



W 



Now let us pull the plates apart, so that d is increased to d f . The 

 electrical energy is now 27rd'(T 2 A, so that there has been an increase of 

 electrical energy of amount 



27TC7 2 J. (d' - d). 



It is easy to see that this exactly represents the work done in separating 

 the two plates. The mechanical force on either plate is 27rcr 2 per unit area, 

 so that the total mechanical force on a plate is 2?rcr 2 J.. Obviously, then, 

 the above is the work done in separating the plates through a distance 

 d'-d. 



It appears from this that a parallel plate condenser affords a ready means 

 of obtaining electrical energy at the expense of mechanical. A more valuable 

 property of such a condenser is that it enables us to increase an initial 

 difference of potential. The initial difference of potential 



4>7rdcr 

 is increased, by the separation, to 



By taking d small and d' large, an initial small difference of potential 

 may be multiplied almost indefinitely, and a potential difference which is 

 too small to observe may be increased until it is sufficiently great to affect 

 an instrument. By making use of this principle, Volta first succeeded in 

 detecting the difference of electrostatic potential between the two terminals 

 of an electric battery. 



REFERENCES. 



MAXWELL. Electricity and Magnetism. Chapter vm. 



CAVENDISH. Electrical Researches. Experiments on the charges of bodies. 236 

 294. 



EXAMPLES. 



1. The two plates of a parallel plate condenser are each of area A, and the distance 

 between them is. d, this distance being small compared with the size of the plates. Find 

 the attraction between them when charged to potential difference V, neglecting the 

 irregularities caused by the edges of the plates. Find also the energy set free when the 

 plates are connected by a wire. 



