In 1832, Gauss made the first absolute measurements of magnetic fields and of magnetic moments in experiments that are straightforward and instructive to replicate. We show, using rare-earth permanent magnets and a variation of Gauss's technique, that the horizontal component of the ambient geomagnetic field, as well as the size of the magnetic moments of such magnets, can be found. The method shows the connection between the SI and cgs emu unit systems for these quantities and permits an absolute realization of the Ampere with considerable precision.
REFERENCES
In geomagnetism, declination means the orientation of the field's horizontal component relative to geographic north, and inclination means its orientation relative to the local horizontal plane.
The distance rc is “critical” only with respect to the torques involved; at the critical separation, and for the orientations used, the force which one magnet exerts on the other is given by −dUint/dr = (μ0/4π) · 3 μ1 μ2 /rc4 ≈ 0.002 N, a small fraction of the weight (0.7 N) of the magnets used.
Each of our magnets is a stack of three cylindrical disks, each of 1.00 in. diameter and 0.25 in. thickness, made of “grade N52” NdFeB material, available as part DX04B-N52 from K & J Magnetics, Inc. (Considerable caution is required for handling these magnets safely, as they can become uncontrollable if allowed within a few cm of steel objects or each other.)
We use 4-pound test line for the vertical support fiber. It is monofilament nylon fishing line of approximate diameter 0.33 mm, with nominal breaking strength 18 N. As the magnets being supported have a weight of only 0.7 N, an even thinner single-strand nylon thread might alternatively be used.
The next-order correction terms (r−5) are of order (size of magnets/separation of magnets)2, which is about 0.1% or smaller due to the compactness of the NdFeB magnets used. By contrast, the original Gauss method reported in Ref. 3 used weak and long steel bar magnets and needed to establish non-zero r−5 and r−7 corrections.
Subsequent measurements at the outdoor location in question using optical pumping of rubidium vapor in the earth's magnetic field established for the local field's horizontal component a value of (19.5 ± 0.1) μT.
We conducted such magnet weighings on a one-pan digital electronic balance using a light non-magnetic support to elevate the magnet above the mechanism of the balance (after confirming the absence of any direct interaction between the Kelvin coil and the balance itself).
