REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1169 



The Field in Free Space 



If no reproducing head is present to disturb the field distribution, the 

 computed field components at a point (ocq , ro) are 



H^ = -4TrIm Sin (27rVX)^o(27rro/X)[(27ra/X)/i(2ira/X) 



-(27raoA)/i(27raoA)] 



(33) 

 Hr = -^irlm Cos (2irVX)i^i(27rro/X)[(27ra/X)/i(27ro/X) 



-(27rao/X)/i(27rao/X)] 

 ro > a 



A discussion and tabulation of the I and K functions can be found in 

 Watson's "Theory of Bessel Functions. "^^ 



The field due to a solid magnetic wire is obtained by setting Oo = in 

 equations {33). This gives 



H, = -^Im Sin (27rVX)(27ra/X)A:o(2WX)/i(27ra/X) 



Hr = -^Im Cos (27rVX)(2xa/X)i^i(27rro/X)/i(27rflA) 



ro> a 



The Rate of Change of Flux in an Idealized Head 



It has not been possible to carry out the calculations for an idealized head 

 which is a satisfactory approximation to the grooved ring-type head often 

 used in wire recording. The results presented below will apply only to repro- 

 ducing heads which completely surround the wire. In this case the idealized 

 head is an infinitely large block of core material of permeability m pierced 

 by a cylindrical hole of radius R in which the wire is centered as shown in 

 Fig. 13. At any point (xq , ro) in the permeable medium the components of 

 flux density can be shown to be 



(35) 



Br= oHr 



ro>R 

 where 



a = 



(36) 



(m - l){2irR/\)lo{2irR/\)Ki{2irR/\) + 1 



and Hx and Hr are given by equation (33). 



12 G. N. Watson, "A Treatise on the Theory of Bessel Functions," p. 79, 361, 698, 

 Cambridge Univ. Press, 1922. 



