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Unformatted text preview: EAD 234A: E&M Homework #6 Due Thursday, February 25, 2010 1. Consider a “gas” comprised of (quasi) independent spin moments s m G (randomly oriented at B = 0) at temperature T. You wish to calculate the their alignment in the presence of an (applied magnetic field B G . It turns out that such alignment is easier for spin moments than for the orbital moments and hence, surprisingly enough, their behavior in the external magnetic field is more “classical”.) Due to the small value of m s ~ μ B , at the ambient temperatures, for all realistic magnetic fields, the orientation energy m s B is much lower than the scale k B T of temperature fluctuations which try to keep spins disoriented so you may assume a Boltzman probability distribution for the spin alignment. Calculate the average magnetization and the magnetic susceptibility χ m . 2. (a) A piece of iron saturates in a magnetic field of ∼ 20; 000 Gauss, when all available electron magnetic moments are aligned. The density of iron is 8 g/cm 3 . How many electrons per iron atom have been aligned to produce this field? (b) You can understand some aspects of the hysteresis curve of a ferromagnet via a model consisting of two permanent dipoles separated by a fixed distance d, but free to rotate. In the absence of any external field, what is the equilibrium orientation and energy of the two dipoles?...
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- Spring '10