1170 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



The total flux through a plane x = ocq in the permeable medium is ob- 

 tained by integrating 



0« = / B^irr) dr 

 Jr 



This gives 

 <i>^ = -2\^odm sin (2TXQ/\){2wR/\)Ki{2TrR/\)[{2Ta/\)Ii(2Ta/\) 



-(2xaoA)/i(2TaoA)] 



(37) 



(38) 



CYLINDRICAL HOLE OF RADIUS R 

 IN INFINITE BLOCK OF PERMEABILITY /t 



Fig. 13 — Round wire surrounded by idealized reproducing head consisting of an 

 infinite block of core material of permeability /x. 



K the plane x = ocq moves with a velocity v with respect to the wire so 

 that xq = vty then 



^ = -iirXavIm cos M{2wR/\)Kii2'!rR/\)[(2Tra/\)Ii{2Ta/\) 

 d^ (39) 



- (2iraoA)/i(27raoA)] 



where w = 2^-/ and / is the reproduced frequency. 



Speclal Cases 



Equation (39) can be used to compute the response of a simple repro- 

 ducing head consisting of a single turn of very fine^' wire as shown in Fig. 14. 



In this case m = 1 and equation (36) shows that a = \. Furthermore if 

 the wire is solid so that oo = 0, equation (39) reduces to 



" Unless the diameter of the wire is small compared to the recorded wavelength there 

 will be additional loss not accounted for by 39. 



