1166 the bell system technical journal, october 1951 



The Flux per Unit Width in the Idealized Reproducing Head 

 The desired flux per unit width is computed from 



<t>x = f B^dz (21) 



Jd+hl2 



where Bx is given by equation (16). Performing the indicated integration 

 gives 



<A. = - ^j 2,r«7„ sin (2,rVX) [ ^ ^J/x^l "'"'" ^^^^ 



If the reproducing head moves past the recording medium with a velocity 

 V so that ocq = z>/, 



d(i>x At . T /I -2irdl\\ -27rd/X 



dt M + 1 



iwviM - e-'^'ne-'''''" cos (coO (23) 



where co is lir times the reproduced frequency. This is the result for unit 

 width of the reproducing head. For a width of W cm., 



% : f- iTWviM - .-^'*'^)e-^'^'^ COS (<./) (24) 



The Case of Perpendicular Magnetization 



Equation (23) was derived for the case of pure longitudinal magnetiza- 

 tion as defined by equations (6). It will now be shown that this same result 

 is obtained for d<t>x/dt if the magnetization is purely perpendicular, that is if 



/« = —Im cos (27rxA) 



(25) 



Ix= ly = 



In this case the divergence of I is zero except at the surface of the tape 

 and this magnetization is equivalent to a surface distribution of magnetic 

 charge on the top and bottom surfaces of the tape. The magnitude of this 

 charge density is just equal to Ig so that on the top surface of the tape there 

 is a surface density of charge given by 



a = -Im cos (27rx/X) at z = 6/2 (26) 



and on the bottom surface of the tape there is a surface density of charge 

 given by 



0- = /m cos (2WX) at z = -5/2 (27) 



Since the permeability of the recording medium is assumed to be unity, 

 this problem reduces to that of finding d^x/dt due to two infinitely thin 



