# bohrmag - angular momentum or spin ± M spin =-g s μ B ±...

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Physics 225/315 January 14, 2008 Magnetic Moments In SI units the classical magnetic moment of a current loop is μ = IA where A is the area of the loop of radius r and I is the current. Then since the current is the charge divided by the period of the motion μ = ev 2 πr πr 2 = emvr 2 m = eL 2 m = e ¯ h 2 m L ¯ h = μ B L ¯ h where L is angular momentum (= mvr ), μ B is the Bohr Magneton, and ¯ h is Planck’s constant divided by 2 π . μ B = e ¯ h 2 m e = 5 . 8 10 - 5 eV / Tesla = 9 . 27 10 - 24 J / Tesla where e is the magnitude of the electron charge and m e is the electron mass. The units of ¯ h are eV-seconds. Check that all the units make sense. We similarly deﬁne the Nuclear Magneton using the proton mass. μ N = e ¯ h 2 M P This classical expression can be taken over for the magnetic moment due to the intrinsic
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Unformatted text preview: angular momentum or spin. ± M spin =-g s μ B ± S ¯ h = γ ± S where g s is called the “g factor” and is approximately 2 for electrons. It diﬀers from 2 by about 1 part in 1000. The g factors for protons and neutrons are rather diﬀerent due to their internal structure. ± S is the spin angular momentum. For electrons, protons, neutrons, and neutrinos the magnitude of the spin is 1 2 in units of ¯ h . The gyromagnetic ratio γ is γ =-g s μ B ¯ h ≈ -2 e ¯ h 2 m e ¯ h =-e m e The force on a magnetic moment is an inhomogeous magnetic ﬁeld is F z = μ z ∂B ∂z...
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