CHAPTER X. 

 SKIN EFFECT. 



IN the last chapter a local quadrature current i( X ) was 

 assumed, whose resistance drop balances up the unequal 

 voltages produced at the center and near the surface by 

 the flux inside the wire. This local current, i (X ), when 

 added up over all parts of the section of the wire, amounts 

 to zero, and so cannot produce magnetic lines in the air 

 outside the wire. But it can produce lines inside the wire, 

 and the effect of these will now be calculated. 



The reactive drop in one wire due to the flux inside it 

 produced by the main current i is 



jwrip 2 Li = janrip 2 X J X IO~ 9 volts, 

 where i is in amperes. 



Then at a distance x from the center we have, from equa- 

 tion (4), Chap. IX, 



janrip 2 . , I . , _ Q jwjri / 9N v 



*(*) = X - X 10 9 - < (p 2 - x 2 ) X 10 9 



r 2 r 



J^L. f _ _ _j_ X 2 \ x IQ -9 



r \ 2 / 



This is a lagging current at the center and a leading 

 current at the surface, and it equals zero when integrated 

 over the entire section. 



The current * (x) , integrated over the circle of radius x, is 



T r x 2J(jyjrH. _Q/ p 2 X . ,\, 



J<) = / X I0 ( - + x ) dx 



Jo r \ 2 / 



.2*2=5 Xltf */_ P^ 2 + - 4 ). 

 r V 4 4/ 



67 



