SKIN EFFECT 69 



Therefore, ^ .. 2L!2^ (fi? _ fi? + 



2 T \2 2 O 



. I corrp 2 IO~ 18 ( x 



U= ~ J 7 2 ~r 



Thus f (, = - "^r" (2 P 4 - 6 p 2 * 2 + 3 * 4 ) (4) 



This current is in phase with the main current and, as it 

 is negative at the center and positive at the surface, it 

 produces a stronger resultant current near the surface of 

 the wire. This is the well-known "skin effect." The 

 effect of the quadrature current i( X ) is to increase the re- 

 sultant current both at the center and near the surface, 

 but its effect is not as large as that of the in-phase current 

 i(2x) and so the net result is a crowding of current toward 

 the surface. 



The above process may be continued indefinitely, each 

 step adding a smaller correction than the one before to 

 the current at radius x and to the average drop in the wire. 



Thus the expression for i (2x ^ equation (4), may be inte- 

 grated over the circle of radius x y and will give the value 

 of 7(2 x ). This current produces a flux density at the radius 

 x, and by integrating this over the outer ring of the section, 

 the value of <t>&x) is obtained. The flux (2 x) produces an 

 unbalanced voltage which must be corrected by a local 

 current z (3x) , so as to give a uniform drop over the section, 

 due to the inductance Z, 3 . Equating the total local current 

 to zero, as before, gives 



T I W IP" 27 



"is" ~7~ 



In the same way it is found that 



. I colO- 36 



