Question

3. A Hall effect probe to measure magnetic field strengths needs to be calibrated in a
known magnetic field. Magnetic fields can be very precisely measured by measuring the
cyclotron frequency of protons. A testing laboratory adjusts the magnetic field until the
proton’s cyclotron frequency is 10.0 MHz. At this field strength, the Hall voltage on the
probe is 0.543 mV when the current through the probe is 0.15 mA. Later, when an
unknown magnetic field is measured, the Hall voltage for the same current is 1.735 mV.
What is the strength of the latter magnetic field

(full answer is needed, well explained please)

Answer 1

A cyclotron is a circular vacuum chamber where the acceleration of particles begins at the center. The particles take a spiral path as they are accelerated.

Convert the units for the frequency from MHz to Hz.

Use the cyclotron frequency to determine the magnetic field strength,

Here, is the mass of the electron, is the charge of electron, and is the cyclotron frequency.

According to Hall Effect, when a magnetic field is applied perpendicular to a current carrying conductor, a potential difference is developed between the points on opposite side of the conductor.

The hall voltage is,

Here, is the charge carrier density, is the charge of the proton, is the conventional current of protons, and is the thickness of the conductor.

Rewrite the equation for.

Substitutefor.

Substitutefor, for,for, for, and for.

Rewrite the equation for.

Substitutefor, for, and for.

Therefore, the strength of the magnetic field is.