94-97] Energy 83 



As a rough approximation, we may still regard the bubble as a uniformly 

 charged sphere, so that if V is its potential, 



a- = 

 and the relation is F 2 = 



giving V in terms of the radius of the bubble, if the tension T is known. In 

 this case the electrification can be made to produce a large change in the 

 radius, by using films for which T is very small. 



Energy of Discharge. 



96. On discharging a conductor or condenser, a certain amount of 

 energy is set free. This may shew itself in various ways, e.g. as a spark or 

 sound (as in lightning and thunder), the heating of a wire, or the piercing of 

 a hole through a solid dielectric. The energy thus liberated has been 

 previously stored up in charging the conductor or condenser. 



To calculate the amount of this energy, let us suppose that one plate of 

 a condenser is to earth, and that the other plate has a charge e and is at 

 potential F, so that if C is the capacity of the condenser, 



e = CV .................................... (29). 



If we bring up an additional charge de from infinity, the work to be 

 done is, in accordance with the definition of potential, Vde. This is equal 

 to dW, where W denotes the total work done in charging the condenser up 



to this stage, so that 



dW=Vde 



p rf p 



= ~- by equation (29). 

 On interation we obtain 



(30), 



no constant of integration being added since W must vanish when e = 0. 

 This expression gives the work done in charging a condenser, and therefore 

 gives also the energy of discharge, which may be used in creating a spark, 

 in heating a wire, etc. 



Clearly an exactly similar investigation will apply to a single conductor, 

 so that expression (30) gives the energy either of a condenser or of a single 

 conductor. Using the relation e = CV y the energy may be expressed in any 

 one of the forms 



........................ (31). 



97. As an example of the use of this formula, let us suppose that we 

 have a parallel plate condenser, the area of each plate being A, and the 



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