42 BELL SYSTEM TECHNICAL JOURNAL 



appears in an a-c. bridge measurement as a resistance 



Pe TrH'fBJAd 

 ' ~ 72" " 6^/2 ^ ^^ ■ ^^^^ 



Substituting for Bm from eq. (6), and for L^ from eq. (4), gives 



47r^/2 



Pe = -y— IJimLmP olim. (11) 



Since this equation contains explicitly no geometrical details of the 

 core, other than the sheet thickness t, it is applicable to any type of 

 core in which the flux density is uniform, as it is in an annular core. 

 If the resistivity is expressed in microhm-cm., the eddy current re- 

 sistance becomes 



p 0.0413/^ 



Re = • fj-mLmP ohm, (12) 



Pi 



A similar solution for the case of a core consisting of a hank or 

 bundle of insulated magnetic wires of diameter / cm. gives 



Re=='^^Ji,,ZmP, (13) 



or with p in microhm-cm., 



„ 0.0155/ , „ ,,,. 



Re = fJimLmf. (14) 



Pi 



A compressed magnetic dust core can be idealized as composed of 

 closely packed insulated spheres. Although there is considerable 

 concentration of flux at various points in any practical core, the 

 power loss in a sphere of diameter /i can be calculated to a first approxi- 

 mation by assuming it permeated by a uniform flux density parallel 

 to the direction of the magnetizing force. Computing the eddy 

 current power loss in a cylindrical shell of such a sphere with shell 

 axis parallel to H, and integrating to obtain the total loss gives 



P = -^\.0-^ (.5) 



The power expended in a cubic centimeter of such a core is then 



Pi = {qI'" X 10-^ (16) 



where t"^ is the mean square sphere diameter, and r is the packing 



