28 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1952 



Hence the magnetic field, H, occurring in Equation (1) is defined by: 

 H = hSi + hlj + hZ 

 and 



M = md + rriyj + {Mz + mz)k 



In solving Equation (1), an exponential, exp [jwt], time dependence 

 is assumed for the alternating magnetic field and magnetization, and 

 if the following assumption is made: 



hx , hy , Ih « Ha 



it is easily shown that the alternating components of the magnetization 

 of the medium are given by (neglecting terms of the second order in 

 small quantities) : 



nix = 



m„ = 



y'Hi\l + a') - co^ + j[2o:yaHi] 

 [y'MzHiil + a) + jyaMz<^]K-\-jyM^K 



(2) 



where : 



Since 



y'Hi\l + a') - c' + j[2o:ycxH:] 

 m^ = 



b = h' -\- 47rw, (3) 



it is possible by means of Equations (2) and (3) to find the relation 

 between the alternating flux density b and the internal alternating field 

 h\ If the ferromagnetic body is considered as being infinite, the internal 

 fields and applied fields are equal. Hence, for this case: 



hx = fiK - jKhy 



by = jKK + t^hy (4) 



b^ = Ih 



where: 



fi = n — Jli 



K = K' - jK" 



