Sec. 3-1] 



MAGNETIC TRA NSDl ( <ERS 



195 



The sensitivity of this method is very high, permitting a measure- 

 ment of magnetic fields of the order of 8 X 10 -6 gauss with a signal- 

 to-noise ratio of 9.7 : 1 . 



The experimental difficulties are considerable. The accelerating 

 voltage, which is of the order of 600 to 1,500 volts, must be kept 

 constant to 1 part in 10 4 . The output current is of the order of 10~ 8 

 amp; for the desired sensitivity 

 the differential amplifier must be 

 built to detect differences in cur- 

 rent of about 10 -12 amp. 



e. Hall-effect Transducers. A 

 plate of an appropriate conductor 

 or semiconductor such as bismuth 

 or germanium is connected to a 

 voltage source as shown in Fig. 

 (3-1)20, so that a constant current 

 / passes through it. Two contacts 



C and D are applied to equipotential points, usually in the middle 

 of the sides. If a magnetic field B traverses the plate in a direction 

 perpendicular to the current vector / and the connecting line CD, it 

 will tend to deflect the moving charges toward the top or the bottom 

 of the plate, depending upon the sign of the charges. Thus, a 

 potential difference, the Hall voltage, will develop between the 

 electrodes C and D, which is 



Fig. (3-1)20. 

 transducer. 



Hall-effect magnetic 



t 



where E H is expressed in volts, / in amperes, B in gauss, and t, the 

 thickness of the plate, in centimeters. K H is the Hall coefficient in 

 volt-centimeters per ampere-gauss. 



The polarity of the output voltage depends upon the direction of 

 the current and of the magnetic field, as well as upon the sign of the 

 Hall coefficient. The dimensions of the plate are not critical. Prac- 

 tical values are 1.2 cm length, 0.4 cm width, and 0.05 cm thickness. 

 The Hall voltage varies somewhat with the ratio of width W to 

 length L of the plate. 1 A ratio WJL = § is recommended. 



The Hall coefficient K H depends upon the material of the plate, as 

 shown in Table 13. The value of K H for bismuth, silicon, and tellu- 

 rium is higher by a factor of about 10 5 than that of most other metals; 

 the value for germanium by a factor of about 10 8 . The values of K H 

 for different substances vary with the amount of impurities. Plates 



1 A. von Ettinghausen and W. Nernst, Wien. Ber., 94, 644 (1886). 



