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Re-creating Gauss's method for non-electrical absolute measurements of magnetic fields and moments
1.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.
2.For a review through 1908 of the state of terrestrial magnetism, see the articles MAGNETISM by Shelford Bidwell and MAGNETISM, TERRESTRIAL by Charles Chree in the Encyclopedia Britannica, 11th ed. (New York, 1911).
4.The historic technique is described in Lehrbuch der Experimentalphysik by E. von Lommel, 22nd edition (J. A. Barth, Leipzig, 1913) at paragraph 148, credited to Gauss (1832).
5. J. E. Fredrickson, “Magnetic field of earth and magnetic dipole measurement—an experiment,” Am. J. Phys. 43, 186–187 (1975), uses Alnico bar magnets and a floating suspension to carry out such a strategy.
6.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.
8.For a highly accessible popular-level introduction to the history of geomagnetism, see North Pole, South Pole, Gillian Turner (The Experiment, New York, 2010).
9.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.)
10.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.
11.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.
14.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.
16.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).
17. Bernard Leroy, “Conversion of electromagnetic quantities from mksa to Gaussian units (and vice versa) using dimensional analysis,” Am. J. Phys. 52, 230–233 (1984).
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