[math-fun] magnetic field strength confusion
The typical saturation magnetic field of stuff like iron, is about 1 tesla. (0.3 to 2.2 teslas more precisely for a selection of commercial materials.) However, the obvious tesla-unitted quantities you construct from the right fundamental constants are far larger: (bohr magneton)*(bohr radius)^(-2)*(elementary charge)^(-2)*(electron mass) =117.526 kiloTesla. Also, e^(-3) * m_e^2 * c^3 * epsilon_0 = 48.1 gigaTesla. If you tried using nuclear masses instead of electron masses, or electron Compton wavelengths instead of bohr radii, these discrepancies would only get huger. (They'd get smaller if you used nuclear magnetons instead of bohr magnetons, but that would definitely be physically wrong since we know ferromagnetism has nothing to do with nuclear magnetism since there is no isotope effect.) Why these enormous discrepancies? -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
Sorry: Actually, turns out there is a simple resolution of this paradox: I should have included mu_0 (permittivity of free space) in my set of fundamental constants: (bohr magneton)*(bohr radius)^(-3)*mu_0=78.64552 Tesla which is only off by a factor of about 40. Now, 40 is still a pretty bothering discrepancy, but it too is resolved if you take into account the fact that the atomic number-density of iron equals 79.48 (bohr radii)^(-3). And then we get 0.9896 tesla, which is a perfectly reasonable estimate of iron's saturation field. Hooray. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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Warren D Smith