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Background
I constructed a fluxgate magnetometer several years ago. It was based upon Richard Noble's article in the September 1991 issue of Electronics World + Wireless World. With a chart recorder, it is possible to see the dirunal changes in the east-west component of the earth's magnetic field, after nulling out the overpowering total and north-south components.
After finding the February 1968 Scientific American article, I thought that it would be an interesting project to try adding a frequency counter to the proton magnetometer.It would be an interesting "backyard science" project to use it to provide a measure of the earth's total magnetic field. The addition of a digital to analog converter can provide a output suitable for a chart recorder.
However, a suburban backyard environment is a rather noisy one. Harmonics of the power line frequency extend well up into the audio frequency range. These compete with the decaying precession frequency tone. Connecting the sensor coils in differential series, sensor orientation and instantaneous sampling of the audio signal help in contending with the noise.
From the physical sciences a quantity called the"Larmor frequency" defines the angular momentum of protons precessing in the presence of a magnetic field.
There are currently quantum-mechanical views that explain particle precession, but a classical explanation seems a bit easier to comprehend. A proton, a charged particle, may be thought of as having definite "spin" about an "axis" and acts as a small magnet. An externally applied magnetic field does not alter the spin rate, but causes the particle to wobble at a slower rate about an axis of precession. This axis tends to align with an external magnetic field. However in weak magnetic fields, any alignment tends toward randomness due to thermal effects and other molecular interactions.
The proton reacts to the perturbing effects of an externally applied magnetic force by precessing at a rate in accordance with a precise constant called the gyromagnetic ratio. For protons this quantity is equal to approximately 267.53 x 1E6 radians per second per Tesla or 42.58 mHz per Tesla.
In the northern latitudes of the U.S. the total magnetic field strength is in the order of 50,000 to 55,000 nanoTesla and varies from location to location. Short period variations due to magnetic storms may reach several hundred nanoTesla. Diurnal variations caused by solar induced ionospheric currents are in the order of tens of nanoTesla. Presently, the long term trend of the total field is in the order of minus 90 nanoTesla per year ( steadily decreasing).
The proton precession frequency detected by a suitable sensor in the geomagnetic field of the earth will be at a frequency in the audio range:
Example:
42.58 mHz / Tesla x 52500 x 1E-9 Tesla= 2235 Hz
In my northeast location the frequency readings currently average about 2271 Hz, corresponding to a total field of about 53,300 nanoTesla. This agrees quite well with the USGS readings shown for the Fredericksburg, VA monitoring station , 160 miles to the west. This figure also agrees with the value obtained using the fluxgate magnetometer that was calibrated using a Helmholtz coil. The fluxgate sensor was tipped upward from a horizontal position to nearly vertical to obtain the maximum reading of the earth field.
I have noticed a decrease in the frequency readings of about six or seven Hertz over the past twelve months or so since the sensors have been in place in the backyard. Originally the frequency readings were around 2277 or 2278 Hz. This also seems to agree with the magnitude of the predicted long term variation shown by the USGS site.