68 TRANSMISSION LINE FORMULAS 



The flux density at the element dx, due to the above cur- 

 rent, is 



IQX lor 



The flux in the ring outside of the circle of radius x, due 

 to /, is 



= 

 10 r 



_ yCOTT^IO" 9 / / pV , P_ 4 _ *_ 4 \ 



lor \ 2 2 4 4/ 



I0 



~ 9 



x 22 



(- p 4 + 2 p 2 * 2 - x 4 ). 



40 r 

 This flux produces a voltage at the element dx, equal to 



IO~ 18 



(l) 



A local current, i( 2x ), will flow in order to keep the volt- 

 age drop uniform over the section. Let the average drop 

 due to 0( X) be 



then 



uVi io~ 18 , *\ f N 



- - (p 4 - 2 p 2 x 2 + # 4 ) + f (2z) r (2) 



Integrate ^ (2 x) over the entire surface and as it is a local 

 current 



2irxi( 2x )dx = o 



uWi iQ- 13 r p , 4 



/ (p 4 * - 2 p 2 * 3 + x 5 ) dx. 

 2 r Jo 



