ELECTROMAGNETIC THEORY OF LINES AND SHIELDS 575 



This is enormous by comparison with the impedance in metals, 

 thereby explaining an almost perfect "electrostatic" shielding offered 

 by metallic substances. Even when the frequency is as high as 100 kc. 

 the radial impedance of air 1 cm. from the source is about 36 X 10^ 

 ohms while the impedance of a copper shield is only 117 X 10~® ohms. 

 The reflection loss is approximately 220 db. 



Power Losses in Shields 



As we have shown in the text under "The Complex Poynting 

 Vector," page 555, the average power dissipated in a conductor is the 

 real part of the integral <J> = 1/2 J^ J' \^EH*2ndS taken over the surface 

 of the conductor. If the source of energy is inside a shield, the 

 integration need be extended only over its inner surface, because 

 the average energy flowing outward through this surface is almost 

 entirely dissipated in the shield, the radiation loss being altogether 

 negligible. If a cylindrical wave whose intensities at the inner 

 surface of the shield of radius "a" are 



H^ = Hq cos n(p, Hp = Ha sin n(p, E, = r]H^, (134) 



7] = iwixajn being the radial impedance in the dielectric, is impressed 

 upon the inner surface of the shield, a reflected wave is set up. The 

 resultant of the magnetomotive intensities in the two is readily found 

 to be {Ikjk + \.)Ho, where k is the ratio of the radial impedance of 

 the dielectric column inside the shield to the impedance Z looking 

 into the shield. If the shield is electrically thick, the impedance Z is 

 obviously the radial impedance of the shield; otherwise it is modified 

 somewhat by reflection from the outside of the shield. The average 

 power loss in the shield per centimeter of length is, then, the real 

 part of 



2irakk*Z TT TT * /1->r\ 



* = (k + m' + 1) "'"'- (1^5) 



This becomes simply 



•I* = iTraZH^H,,*, (136) 



if the frequency is so high that k is large as compared with unity. 



If the source of the impressed field is a pair of wires along the axis 

 of the shield, the magnetomotive intensity on the surface of the shield 

 can be shown to be 



H^ = - — •„/ cos (p, (137) 



