8. Curie susceptibility: consider N non-interacting quantized spins in a magnetic field B = Bê, and at a temperature T. The work done by the field is given by BM,, with a magnetization M, =µE m,. For each spin, m, takes only the 2s+1 values -s, -s+ 1,....s-1, s. (a) Calculate the Gibbs partition function 2(T, B). (Note that the ensemble corresponding to the macrostate (T, B) includes magnetic work.) (b) Calculate the Gibbs free energy G(T, B), and show that for small B, Nu²s(s+1)B² G(B) = G(0) – +0(B*). 6k„T (c) Calculate the zero field susceptibility x= aM,/jƏB[B-0, and show that it satisfies %3D Curie's law

8. Curie susceptibility: consider N non-interacting quantized spins in a magnetic field B = Bê, and at a temperature T. The work done by the field is given by BM,, with a magnetization M, =µE m,. For each spin, m, takes only the 2s+1 values -s, -s+ 1,....s-1, s. (a) Calculate the Gibbs partition function 2(T, B). (Note that the ensemble corresponding to the macrostate (T, B) includes magnetic work.) (b) Calculate the Gibbs free energy G(T, B), and show that for small B, Nu²s(s+1)B² G(B) = G(0) – +0(B*). 6k„T (c) Calculate the zero field susceptibility x= aM,/jƏB[B-0, and show that it satisfies %3D Curie's law

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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