1 70 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



in which k is the inductivity of the dielectric, x is the thickness 

 of the dielectric in centimeters, and a is the area in square 

 centimeters of one plate of the condenser (sectional area of the 

 dielectric). 



92. Work done by an electromotive force in pushing a given 

 amount of charge through a circuit. Consider an electromotive 

 force E maintaining a current / in a circuit. The rate at 

 which this electromotive force does work is equal to El, which, 

 multiplied by a time /, gives the work done during that time, 

 so that W= Elt. But the product It is equal to the charge q 

 which is transferred during the time t, therefore we have 



W=Eq (64) 



in which W is the work done by an electromotive force E dur- 

 ing the time that charge q is pushed through the circuit. The 

 work W is expressed in joules when E is expressed in volts 

 and q in coulombs. 



93. The potential energy of a charged condenser. A charged 

 condenser represents a store of potential energy in much the same 

 way that the distorted diaphragm DD in Fig. 104 represents a> 

 store of potential energy, or in the same way that a bent spring 

 represents a store of potential energy. When a spring is bent, 

 the bending force is at first equal to zero, it increases in propor- 

 tion to the amount of bending, and the average value of the 

 bending force is equal to one half its ultimate value (that is, the 

 value which corresponds to a given amount of bend). Let E 

 be the ultimate value of the bending force and q the distance 

 through which the end of the spring is moved, then \E is the 

 average value of the bending force, which, multiplied by q, gives 

 the work done in bending the spring or the potential energy of the 

 bent spring. Therefore, the potential energy of the bent spring 



is given by the equation 



W=\Eq 



in which E is the ultimate value of the bending force, and q is 



