1152 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



through the ring of Fig. 5 and can be made to thread through a coil of many 

 turns wound on the ring. In so far as this is true, calculations based on this 

 bar type head are applicable to ring type heads. 



If the bar of Fig. 4 is now allowed to become infinite in length, width, 

 and thickness, the flux density in it can be computed and the flux per unit 

 width can be evaluated. This calculation is outlined in Appendix I. If the 

 tape moves past the head with a velocity v in the x direction, the repro- 



SINGLE TURN OF 

 VERY FINE WIRE 

 \ 



BAR OF PERMEABLE 

 MATERIAL 



SPACING d 



Fig. 4 — Idealized bar-type reproducing head. 



Fig. 5 — Idealized ring- type reproducing head. 



duced voltage should be proportional to the rate of change of flux. In the 

 appendix this is shown to be 



dt 



2t«/X\ -2-Kdl\ 



M+1 



^irlVvIrr^iX - e-''"le 



cos 



(co/) 



(3) 



d4>x . 



where ^ is the rate of change of flux in W cm. width of the reproducing 

 dt 



head measured in Maxwells per sec, 



H is the permeability of the reproducing head, 



W is the width in cm. of the reproducing head (and of the recorded 



track in a practical case), 



