280 ELECTROSTATICS. [PT. II. CH. VI. 



and on the plate 2, 



<7 



4-7T V 9-3 JZ=T 4-7TT 



The charge on an area 8 of either plate is 



The capacity of the condenser is 



47TT 



agreeing with the results in the two preceding cases. 



In fact, for any condenser in which the two plates are separated 

 by a small distance, which is the same over the whole of their 

 opposed surfaces, we may use the above value for K. 



146. Standard Condensers. For the purpose of furnish- 

 ing a standard of capacity or for measuring quantities of electri- 

 city when their potentials are known, condensers of one of the 

 three forms just described, viz., plates, cylinders, or spheres, are 

 nearly always used. The spherical condenser is the only one for 

 which our formulas are exact, for in the other two cases some of 

 the dimensions have been supposed infinite, and we have dis- 

 regarded the charges on the backs of the plane plates, or on the 

 outside of the outer cylinder. This difficulty is surmounted in the 



B 



FIG. 58. 



following manner. If a portion of the plate A (Fig. 58) be separated 

 from the surrounding portion C by a narrow cut, but be placed in 

 conducting connection with C, the charge on A, if the edge of the 

 outer portion C is sufficiently remote, will be that calculated, for 



