The Hall Effect With Audiofrequency Currents

Abstract

Hall e.m.f. in tellurium for currents of frequencies up to 25,000 cycles per sec.—The Hall e.m.f. in tellurium has been investigated with currents of frequencies up to 25,000 cycles per second, with particular reference to any effect of frequency on the magnitude of the Hall coefficient $R_H$, and on the phase of the Hall e.m.f. relative to the longitudinal current producing it. A Hartley-circuit vacuum-tube oscillator furnishes the current for the specimen, which is placed in a constant magnetic field of about 3000 gauss. The Hall e.m.f., amplified by a resistance-coupled vacuum-tube amplifier, is observed on a cathode-ray oscillograph. A general method of procedure is indicated for use in comparing alternating e.m.f.'s as small as a few millivolts or less with respect to magnitude and phase. The current drawn and the power consumed are entirely inappreciable. The results of a comparison method of this sort and a null method agree in the conclusion that in the range studied, the Hall coefficient for tellurium is constant to within about 2 percent for frequencies up to 10,000 c.p.s. and to within 7 percent for the complete range. This agrees with the results of Smith on bismuth. For the specimen used the value found for the Hall coefficient is $R_H=481\mathrm{}$. The two methods also agree in finding the frequency, wave-form, and phase of the Hall e.m.f. the same as those of the longitudinal current producing it. The phase difference, if any, is believed to be less than 2° at frequencies below 20,000 c.p.s. and less than 4° at 25,000 c.p.s.