REDUCTION OP SKIN EFFECT LOSSES 



519 



(ff.)„ = -iiy -d) 



(VI-3) 



{HX = ( - 1)""' g) nr sin [(nr + | A) 5^^] (vi-4) 



The current densities for w = 0, 1, 2 are shown in Fig. 12. We see that the 

 current density for « = is all of one phase, while for the higher modes 

 the current density has one or more reversals of phase. For these higher 



Fig. 14 — Current distribution in completely filled line for various modes. 



modes, the net current in the laminae is essentially zero and consequently 

 we should expect only small fields in the interior of the line. This supposi- 

 tion is confirmed in Fig. 13, where the magnetic fields in the laminae are 

 drawn for w = 0, 1, 2. The fields for all the modes have a common value 

 unity Sit y = s, but for the higher modes the fields in the interior of the 

 laminae are much greater than unity. 



For the completely filled Une, we have from equation (V-12) 



nw . mry 



(VI-5) 



