A magnet suspended in a uniform magnetic field like that of the Earth can be made to oscillate about the field. The frequency of oscillation depends on the strength (magnetic moment) of the magnet, that of the external field, and the moment of inertia of the magnet. It is easily shown and verified by experiment that a simple but nontrivial expression represents this motion well, but that only the product of the magnetic moment and magnetic field can be determined. The repulsion of two magnets can be used to determine the magnetic moment, and in turn the external field can be determined. The results are reasonably good considering the very simple equipment required, and the experiment allows quantitative investigation of magnetism.
REFERENCES
1.
The torque on a coil is derived in Chap. 20 of D. Giancoli, Physics, 6th ed. (Pearson Prentice Hall, Upper Saddle River, NJ, 2005), and the relation to permanent magnets is explained.
2.
This result follows immediately by solving the equation of motion with calculus; a noncalculus discussion of various types of harmonic oscillators is found in Chap. 13 of J. Touger, Introductory Physics: Building Understanding (Wiley, New York, 2006).
3.
See the recent TPT article by
Mike
Moloney
, “Strong little magnets
,” Phys. Teach.
45
, 352
–355
(Sept. 2007
) and an earlier, related article by
G.
Hageseth
, Am. J. Phys.
37
, 529
–531
(May 1969
). The magnets used in this experiment were purchased at Lee Valley Tools' local store, but similar magnets are now widely available.4.
If allowed to pivot freely about the center of mass, a dip indicator would result. These were historically used as scientific instruments, including on expeditions to find the north magnetic pole (the “dip pole”). Usually the form was like a vertical compass or “dip needle”. See http://physics.kenyon.edu/EarlyApparatus/Electricity/Dip_Needle/Dip_Needle.html.
5.
See, for example, D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics, 8th ed. (Wiley, New York, 2007), p. 253.
6.
This is known as paramagnetism; the opposite behavior, diamagnetism, is also possible. Deeper understanding of magnetism is based on advanced concepts. Reading accessible to those slightly beyond the first year level can be found in the Feynman Lectures on Physics, Vol. II (Addison Wesley, Reading, MA, 1964).
7.
http://www.vernier.com gives information about this inexpensive and useful program.
8.
If SI units are consistently used, the details of the complex magnetic units can be avoided.
9.
The magnetic field very near the magnet is in general quite complex, although it may have some simplifying characteristics such as symmetry
10.
This is a modification of the spherical coordinate form given in P. Lorrain and D. Corson, Electromagnetic Fields and Waves, 2nd ed. (Freeman, New York, 1970) in Chap. 7.
A more exact form based on the magnetization of the magnet and its dimensions is given by
M.
Connors
, “Measurement and analysis of the field of disk magnets
,” Phys. Teach.
40
, 308
–311
(May 2002
) and could be reworked to allow to be determined by measuring the magnetic field along the axis. However, the intent here is to use minimal instrumentation.11.
J.D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 185.
12.
Earth field measurements are usually given in units of nanotesla (nT).
13.
http://gsc.nrcan.gc.ca/geomag/field/magref_e.php leads to the International Geomagnetic Reference Field and also the version specific to Canada.
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© 2007 American Association of Physics Teachers.
2007
American Association of Physics Teachers
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