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 9.70 MHz . At this field strength, the Hall voltage on the probe is 0.547 mV when the current through the probe is 0.160 mA . Later, when an unknown magnetic field is measured, the Hall voltage at the same current is 1.733 mV .

Part A

What is the strength of this magnetic field?

???? T

Explanation / Answer

Cyclotron frequency is given by:

f = 1/T

T = 2*pi*r/V

r = m*V/qB

T = 2*pi*m/qB

B = 2*pi*m/(q*T) = 2*pi*f*m/q

Using givne values:

B = 2*pi*9.70*10^6*1.67*10^-27/(1.6*10^-19)

B = 0.636 T

Now Hall Voltage is given by:

Vh = i*B/(n*q*L)

Since i and L are constant So

Vh2/Vh1 = B2/B1

B2 = B1*(Vh2/Vh1)

B2 = 0.636*(1.733/0.547)

B2 = 2.015 T

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