1338 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



2Trrdr. The resistance of the wire in R t = p,P2l/T-[pi{r2~ — Vi") -\- po/'i']- 

 The observable voltage for a length of wire, /, is 



Fobs = / [Vir)] (Volt-Divider) 



Pl/32^ 



f'-2 - >'i \ y/Q) 7r[pi(r2- - ri^) + p^rj^] 



2Trr dr 

 P1P2I 



+ / ' (^''^ " ') 7(0) ' ^^P^'^^^' ~ ''1') + P''^'^^ 





r-i ) \ P2I 



27rr dr 

 This reduces to 



(1 - a^)pi/p2 + a- 

 = 6F(0), (30) 



where a = ri/r-i and b is given by reference to (29). The ratio b/^ = 36 

 is the relative efficiency of the composite as compared to the solid 

 magnetic wire from an available signal viewpoint. An expression for s„, 

 will now be derived. 



The total energy dissipated per unit length I is 



^r/l = Ts r pij{r)2wr dr, (31) 



Jo 



''•2 



where idir) is the current density. Now, ij{r) = Y{r) — T''obs/p/, therefore 



i,{r) = (1 - a - b)^, < r < r^ 



pit 



= 11 — — — 1 — — /'i < /■ < ro 



\ r2 / p2i 



The substitution of (32) into (31) yields, after manipulations. 



(32) 



?av/« 



_ TT^r/ (Vm\ / 2 



P. y^lTl 



4a(l - 5) a 



(1 -a-6)^'^-?-(l -6)^ 

 Pi 



+ 



3 2 



+ a-«=-W^ + ^] 



(33) 



