ELEMENTS OF ELECTRICITY AND MAGNETISM. 



When a battery is connected to the terminals of a condenser 

 the full electromotive force of the battery begins to act at once, 

 and the current surges back and forth through the circuit until 

 the system finally settles to equilibrium. When this final state 

 of equilibrium is reached, a definite amount of charge q will 

 have been pushed into the condenser by the battery, and the 

 total amount of work done by the battery will be Eq ; but the 

 amount of potential energy stored in the condenser is %Eq, and 

 therefore an amount of work \Eq has been dissipated by the 

 electrical oscillations of the system, exactly as in the case of the 

 spring and weight above described. 



In order that all the work done in stretching a spring may be 

 stored in the spring as potential energy, the stretching force must 

 begin at zero and increase gradually as the spring is bent more 

 and more ; in order that all the work done in charging a con- 

 denser may be stored in the condenser as potential energy, the 

 charging electromotive force must begin at zero and increase 

 gradually as the condenser becomes charged. If the final value 

 of the charging electromotive force is E its average value is 

 \E, which, multiplied by the amount of charge q that has been 

 pushed into the condenser, gives the potential energy of the 

 condenser. 



The potential energy of a charged condenser may be expressed 

 in terms of E and q, or in terms of C and E, or in terms 

 of C and q by using equation (61). Thus, by substituting 

 CE for q, equation (65^) becomes 



and by substituting qJC for E, equation (650) becomes 



94. Transference of charge by a moving ball. Intensity of elec- 

 tric field. Two metal plates A and B, Fig. 106, are con- 

 nected to a battery of which the electromotive force is E, and a 



