A BRAUN TUBE HYSTERESIGRAPH 



303 



Let the true cycle of magnetization of the sample be that shown in 

 Fig. 11. Let the magnetizing field be sinusoidal, //' = Hi cos wt, so 



Fig. 11 — Simplified hysteresis loop. 



that the rate of change of the field in the region where the induction 

 is variable is nearly 



dH' . 



-IT = "^^- 



When the induction is varying there is a reverse magnetizing field set 

 up by the current in the search coil of the strength 



47r 

 AH = -10- 



mS ^ _ 47r 

 IR dt ~ 10 



ms dB dH 

 IR dH dt ' 



The value of dH/dt is not known, since it itself involves AH, but its 

 maximum value is {dH' /dt) = wHi. The reverse field is, therefore, 

 at the most 



A// = -10- 



mS dB ^ 

 iR dH ''^'■ 



(15) 



The calculation of AH has been done for a number of cases. With 

 the ring shaped samples having search coils of 90 to 135 turns the 

 value of AH was .1 per cent of the coercive force He for iron, and 

 4 per cent of He for permalloy. When a permalloy having a thin 

 hysteresis loop with the slope (dB/dH) = 200,000 is used in the search 

 coil of 30,000 turns, the value of AH is nearly as large as He so that 

 the curve is approximately doubled in width. In such a case the fac- 

 tor N'^S/IR must be made smaller, preferably by decreasing A^'^ since 

 this does not involve a corresponding increase in the amplification. 



It must be remarked that these formulae give the maximum errors, 

 and that in fact the errors are considerably less. The condenser 

 across the magnetizing coil permits the magnetizing current to take 

 other than sinusoidal form, so that the value of dH/dt is much 

 smaller than coHi. 



