158 



STATIC ELECTRICITY 



Let us take such a system as a condenser with one surface earthed 

 and with the other connected to a source at potential x where x 

 can be varied at will. Let the charge at x be m. Let the plates 

 of the condenser be / apart and let them be subjected to force F, 

 compressing the dielectric. Then in changing the length /, work 

 Ydl is done. Let the temperature be kept constant so that in any 



cycle j dQ = 0, where dQ is an element of heat imparted. Then, on 

 the whole, no heat is converted into work or vice verm during a 

 cycle, and we have only to consider the interchange of energy 

 between the electrical form and that represented by the work done. 

 If E is the electrical energv, the principle of the conservation 

 of energy gives in any cycle 



Further, we assume that the charge m is a definite function of the 

 condition of the system, there being no leakage, and so when we go 

 through a cycle 



/dm = 0. 



Lippmann termed this the principle of the conservation of 

 electricity. 



Now let us represent the system on a diagram in which abscissae 

 represent / and ordinates F, so that areas represent work done, 

 Fig. 106. The dependence of m on the physical condition implies 



that we can draw a series of equal charge lines on the diagram, such 

 as AD at charge m-dm and BC at charge m. Further, the potential 

 will be a definite function of the physical condition, for it is equal 

 to charge /capacity, each term of which is such a function. Hence 

 we can draw a series of equipotential lines, such as A B at tf, and 

 DC at x-dx. These lines are analogous to isothermal?, and the 

 equal charge lines to isentropics on the ordinary indicator 

 diagram. 



