302 ELEMENTS OF ELECTRICAL ENGINEERING. 



radius of the metal sheath, E is the electromotive force in volts between the centra 

 wire and the sheath, and Log e R 2 IR\ is the Naperian logarithm of the ratio R^R Y 



Maximum electric stress in the medium between parallel wires. Let R be the 

 radius of each wire, and d the distance from center to center. The electric field in- 

 tensity ( volts per centimeter) at a point, p y on the line, //, distant x from the center of 

 W and distant d x from the center of W ff t see Fig. 172, consists of two parts, f f 



d \ 



Fig. 172. 



and /", which are proportional to I/JT and to \l(d x) respectively, so that we may 

 write : 



/-! (o 



and 



These two equations are only approximately true unless the distances x and 

 d x are measured from points a very little closer together than the axes of the two 

 wires. When, however, R is small in comparison with d, it is sufficiently exact to 

 measure x and d x from the axes of the wires. 



The electromotive force E between the wires is : 



E = 



Therefore, using the values of f and/" from equations (i) and (ii), we find, by 

 integration : 



or, since R is usually small in comparison with d, this equation may be written : 



whence 



.- E 



(iv) 



Now the region of greatest intensity of the electric field is at the surface of one (or 

 the other) of the wires where x = R, and where 



d R 



