72 TRANSMISSION LINE FORMULAS 



Chap. IX.) Let it take up such a distribution that the 

 drop at all parts of the section of the wire, due to re- 

 sistance and to magnetic flux, is the same. Then if i r be 

 the current density at radius x, we may assume 



*' x = OQ + aix 2 + a^x* + + a n x 2n + (8) 



where a , 0i, . . . a n , etc., are constants, independent of x. 

 (As the same value of i' would be obtained for both +x 

 and x, only even powers of x need be assumed for the 

 series.) 



The total current in the part of the section inside a 

 circle of radius x will be 



/' 



= / 2irxi f dx 



Jo 



2 4 2n 



The flux density at the radius x is 



10 



and the total flux in the outer ring of the section, outside 

 the circle of radius x, is 



'= C P 

 J x 



TT / 2 . ai# 4 . . . n - . 



-- a ^ 2 H -- - + -~- + +- z -- h 

 io\ 2 2 3 2 w 2 



The drop at radius x due to the flux r is 



ja4>' X io~ 8 

 and the resistance drop due to the current at the same 



