1164 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



The problem of most interest is that of finding the x component of mag- 

 netic induction, Bx , at any point {xo , Zo) in the ideahzed head and inte- 

 grating this with respect to Zo to determine the total flux passing through 

 unit width (in the y direction) of a plane x = xo . This plane will then be 

 allowed to move with a velocity v by putting Xq = vt and the time rate of 

 change of flux will be computed. Except for the effects of eddy currents, 

 self demagnetization, gap loss, etc. (which are treated separately) this rate 

 of change of flux should be proportional to the open circuit reproduced 

 voltage. This is the only result of which direct use will be made but for the 

 sake of completeness all the field components will be evaluated not only in 

 the idealized head but also at all other points. 



This problem is completely analogous to the problem of a point charge in 

 front of a semi-infinite dielectric treated by Abraham and Becker^^ and can 

 be solved by use of the method of images. 



The Field Inside the High Permeability Head 



By analogy with the treatment of Abraham and Becker, the value of B 

 in the high permeability head is computed as though this head filled all 

 space and as though the recording medium were polarized to a value 

 2/i/(/Li +1) times the actual value of polarization present. This gives di- 

 rectly from equations (12), 



B. = -[2m/(m + mTTlm sin (2TXo/\)e-''''''\e''"^ - e""^) 



B, = -[2/z/(m + m^Im cos (27rVX)^"''^'^''(^'^''' - ^"'''') 

 Zo > ^ + 8/2 



The Field Below the Reproducing Head 



Again by analogy with the treatment of Abraham and Becker, the field 

 outside the idealized head is computed as though no head were present. 

 The field is that due to the actual magnetized medium plus the field due to 

 an image of the medium (centered about z = 2d -{- 8). The intensity of 

 magnetization of the image medium is — (/u — 1)/(m + 1) times the in- 

 tensity of magnetization of the actual medium. 



The field due to the image medium is computed from equations (13) 

 after suitable modification. The required modifications are: 



1. Multiply the right hand sides by — (/x — 1)/(m + 1) to take account 

 of the magnitude and sign of the image magnetization as just dis- 

 cussed, and 



2. Replace zc by So — (2d -\- 8) io take account of the position of the 

 image. 



" M. Abraham and R. Becker, The Classical Theory of Eleclricily and Magnetism. 

 |). 77, Blackie and Son Limited, London, 1937. 



