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Unformatted text preview: Physics 225/315 February 4, 2008 Magnetic Moments, Energy Levels In SI units the classical magnetic moment of a current loop is = 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 = ev 2 r r 2 = emvr 2 m = eL 2 m = e h 2 m L h = B L h where L is angular momentum (= mvr ), B is the Bohr Magneton, and h is Plancks constant divided by 2 . 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. Check that all the units make sense. 1 eV = 1 . 6 10 =19 J hc = 1240 eV- nm hc = 200 eV- nm m e 1 / 2 MeV M p 940 MeV We similarly define the Nuclear Magneton using the proton mass. N = e h 2 M P This classical expression can be taken over for the magnetic moment due to the intrinsic angular momentum or spin. M spin =- g s B S h = 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 is =- g s 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...
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