IDEA OF POTENTIAL. 173 



With any other dielectric the capacity is k times as great where 

 k is the inductivity of the dielectric. 



103. Maximum electrical stress in cable insulation. Consider 

 a portion / centimeters in length of an electric cable. Let RI 

 centimeters be the radius of the central wire, let RZ centimeters 

 be the inside radius of the lead sheath, let k be the inductivity 

 of the dielectric and let E volts be the electromotive force be- 

 tween central wire and sheath. It is desired to find an ex- 

 pression for the electrical stress e in volts per centimeter at 

 the surface of the central wire, this being the place where the 

 electrical stress is a maximum. The capacity of unit length of 

 the cable is given by equation (5) of Art. 102, and the capacity of 



/ centimeters of the cable is / times as great, or 



> 



*.(!) 



Multiplying this by E we get the number of coulombs on / 

 centimeters of the central wire, and multiplying the number of 

 coulombs by B we get the electric flux emanating from the / 

 centimeters of the central wire according to Gauss's theorem 

 (Art. 86). But the electric flux density at the surface of the 

 central wire is ke according to Art. 86, and the area of / centi- 

 meters of the central wire is 2irRil so that the electric flux ema- 

 nating from / centimeters of the central wire is 2wRil X ke. 

 Therefore, placing these two expressions for the electric flux 

 equal to each other we have: 



2TTIBE k 



2,RJke = - ---- (i) 



from which we get: 



- E 



^at surface of central wire 



1 Ml) 



104. Capacity of parallel cylindrical wires in air. The capacity 

 of a two- wire transmission line in farads per mile of double line is : 



