1320 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



First, consider the case in which the magnetization is entirely circular. 

 Reversal from one flux remanent state to the other is assumed to occur 

 uniformly in time Ts . Axial eddy currents will flow down the center of 

 the wire and return along the surface. The switching coefficient, Sw , 

 will be obtained by equating the input energy to the dissipated energy . 

 The total energy dissipated per unit length is, 



8 = n f " 27rrP(r) dr, (4) 



Jo 



and 



pw=Mr)l\ (5) 



P 



where P(r) the power density is given by E{r) the voltage gradient 

 squared divided by the resistivity. The average energy per unit volume 

 is therefore 



Sav/cm3 — 5 / ^^ 27rr (//' 



Trro ^0 



P^' " ■ (6) 



^ T^ /my 



18pV I J 



Now F(0) = [{dB/dt)rd]\^~\ so F(0)// = (25,ro/n)10^l Putting this 

 expression into (6) yields 



2 2 



_ 2Bs Vq 16 ,-,s 



Oaver/cm^ — —x — jf^ — i.\J . \l ) 



The input energy per unit volume is 



. 3 (25,i/cos0i) 10"' .„. 



S/cm = , (8) 



47r 



since ABH = 2BsH cos 9i where di is the angle betw^een the applied 

 field H and the switching flux. The factor 10~ /47r is a constant relating 

 the energy in joules to the BH product in gauss-oersteds. By equating 

 (7) and (8), and replacing H hy {H — Ho), the desired s,„ expression is 

 obtained ; 



s^ = T.{H - Ho) = (^TnB.ro^) 10 ' ^^^_^^^^^^ (9) 



\)p cos ^1 



The substitution oi H — Ho for H requires some explanation. The 

 switching curve of \/Ts versus H is not a straight line as would be pre- 



