REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1165 



This gives the field due to the image plane as 



//xi = 27r/m , , sin {2'KXQ/K)e " {e ' - e ) 



" + ' (17) 



Hzi = — lirlm ' — ;— 7 COS (27r.r()/X)e (e — e ) 



M + 1 



2o < (/ + 5/2 



To this must be added the field due to the real medium which is given by 

 equations (12) when h/2 < Zq < d -{- 5/2, by equations (15) when —5/2 < 

 Zo ^ 5/2, and by equations (13) when Zq < —5/2. 



Performing this addition gives the following results: 



Between the head and the recording medium, 



H. = -2irl„. sin {2irXo/\)e-'''''\e^''^ - e'^"^) 



[. M -" 1^ -2T(2d+4-2zo)/X 



(18) 



d -{- d/2 > Zo > 5/2 

 Inside the recording medium, 

 Hx = — 2irlm sin {2irXo/\) 



[2 _ -»5/X/g2r^o/X , ^-2tjo/X\ _ M_"" J ^-2x(2d+«-zo)/X/gT5/X _ ^-'i/Xj 



i7, = -27r/^ cos (27rV^) (^'^) 



[-x6/\/ 2T20/X _ -2tzoI\\ , M ~ 1 ^-2r(2d+S-zo)/X/ »-a/X _ g-»«/X\ 

 M 4- 1 J 



5/2 > 2o > 5/2 



Below the recording medium, 



Hx = -27r/.sin (27rWX)^''"''(^'''' - e''"') 



r M — 1 -2r(W4«)/xl 



■ L^ " 7+"i J 



Z/, = 2,/„ cos (2TX,/\)e""%"" - e-'") (20) 



^"r+"i' J 



2« < -V2 



