130 ADVANCED ELECTRICITY AND MAGNETISM. 



abscissas and ordinates respectively, we will get a straight line 

 cc as shown in Fig. 88. 



Consider the total amount of work W which is done while the 

 spring is being stretched from g = o to q = Q, and while the 

 stretching force is increasing from e o to e = E. The aver- 

 age value of the stretching force is \E, as may be understood 

 from Fig. 88, and the work done is equal to the product of the 

 total stretch Q and the average stretching force \ E. That is : 



W= 



and this work W is stored in the stretched spring as potential 

 energy. Thus a stretch of 3 feet ( = Q) is produced in a large 



spring, and the stretching force 



* w rises from zero to 60 pounds 



( = E) . The average value of 

 the stretching force is 30 pounds 

 (= i-E), the work done is 

 90 foot-pounds (= \EQ)\ and 

 this work is stored in the 

 stretched spring as potential 

 energy. 



Suppose a condenser to be charged by applying it to an elec- 

 tromotive force which begins at zero and rises to E volts, then 

 the amount of work W which is done in charging the condenser 

 is equal to \EQ where \E is the average value of the charging 

 electromotive force, and Q is the total charge which is drawn 

 out of one plate of the condenser and pushed into the other 

 plate. This statement is in accordance with equation (i) of 

 Art. 80. Therefore: 



W = \EQ (i) 



where W is the potential energy of a charged condenser, E is 

 the voltage acting on the charged condenser, and Q is the charge 

 which has been drawn out of one plate of the condenser and 

 pushed into the other plate; W is expressed in joules when E 

 is in volts and Q in coulombs. 



