A Hall-effect probe to measure magnetic field strengths needs to be calibrated i

Question

A Hall-effect probe to measure magnetic field strengths needs to be calibrated in a known magnetic field. Although it is not easy to do, magnetic fields can be precisely measured by measuring the cyclotron frequency of protons. A testing laboratory adjusts a magnetic field until the proton's cyclotron frequency is 10.3 MHz . At this field strength, the Hall voltage on the probe is 0.546 mV when the current through the probe is 0.154 mA . Later, when an unknown magnetic field is measured, the Hall voltage at the same current is 1.731 mV . Problem 29.68 A Hall-effect probe to measure magnetic field strengths needs to be calibrated in a known magnetic field. Although it is not easy to do, magnetic fields can be precisely measured by measuring the cyclotron frequency of protons. A testing laboratory adjusts a magnetic field until the proton's cyclotron frequency is 10.3 MHz. At this field strength, the Hall voltage on the probe is 0.546 mV when the current through the probe is 0.154 mA . Later, when an unknown magnetic field is measured, the Hall voltage at the same current is 1.731 mV . Part A What is the strength of this magnetic field? Express your answer with the appropriate units. alue Units Submit My Answers Give Up Continue

Explanation / Answer

Cyclotron frequency is given by

f=qB/2pim

Therefore Magnetic fiele strength is given by

B=2pimf/q =2pi*(1.6727*10-27)*(10.3*106)/(1.6*10-19)

B=0.6766 T

Hall Voltage is given by

VH=IBD/nqA

=>V2/V1 = B2/B1

B2=(1.731/0.546)*0.6766

B2=2.14 T

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