Posted by Troubled student on January 19, 2013, 10:28 pm
Given that the energy of an electron in a magnetic field is +/- mu_b*B, we argue that the magnetization M = -1/V dE/dB = -(# up spins - # down spins)*mu_b/V. We then argue that the quantity (# up spins - # down spins) is proportional to B, so we get M is proportional to B. However, if we put in our value for (# up spins - # down spins) before we do the differentiation dE/dB, then we are differentiating B^2, so we get M is proportional to 2B. Is there something wrong with doing it this second way? It introduces a factor of two which isn't present in the first method... hopefully what I've said makes some sense =) Thanks!
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