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 0.540 mV when the current through the probe is 0.158 mA. Later, when an unknown magnetic field is measured, the Hall voltage at the same current is 1.731 mV. What is the strength of this magnetic field? Express your answer with the appropriate units.

Explanation / Answer

You should be aware that magnetic field and flux density (if that is in fact what you mean) are vector quantities, and are incompletely specified unless their direction is stated. This means that since the direction of the 'unknown' field with respect to the known field is in fact unknown, we cannot answer the question. Have a word with your teacher about vector quantities and how they should be specified.

However, if we assume that the direction of the unknown field is the same as that of the known one, then we can say that the Hall voltage will be proportional to the magnitude of the flux density, the Hall current remaining the same. This makes the unknown field 1.731/0.540 times as strong as the known one. This ratio is 3.205 to 3dp.

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