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Problem 1.6.5. A magnetic moment µ in a magnetic field h has energy E+ = Fµh when it is parallel (antiparallel) to the field. Its lowest energy state is when it is aligned with h. probabilities for being parallel or antiparallel given by P(par)/P(antipar) = exp(-E+/T]/ exp[-E-/T] where T is the absolute temperature. Using the fact that the total probability must add up to 1, evaluate the absolute probabilities for the two orientations. Using this show that the average magnetic moment along the field h is m = µ tanh(uh/T) Sketch this as a function of temperature at fixed h. Notice that if h = 0, m vanishes since the moment points up and down with %3D However at any finite temperature, it has a nonzero %3D equal probability. Thus h is the cause of a nonzero m. Calculate the susceptibility, dm lh=0 as a function of T.

Problem 1.6.5. A magnetic moment µ in a magnetic field h has energy E+ = Fµh when it is parallel (antiparallel) to the field. Its lowest energy state is when it is aligned with h. probabilities for being parallel or antiparallel given by P(par)/P(antipar) = exp(-E+/T]/ exp[-E-/T] where T is the absolute temperature. Using the fact that the total probability must add up to 1, evaluate the absolute probabilities for the two orientations. Using this show that the average magnetic moment along the field h is m = µ tanh(uh/T) Sketch this as a function of temperature at fixed h. Notice that if h = 0, m vanishes since the moment points up and down with %3D However at any finite temperature, it has a nonzero %3D equal probability. Thus h is the cause of a nonzero m. Calculate the susceptibility, dm lh=0 as a function of T.

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Problem 1.6.5. A magnetic moment µ in a magnetic field h has energy E+ = Fµh when it is parallel (antiparallel) to the field. Its lowest energy state is when it is aligned with h. probabilities for being parallel or antiparallel given by P(par)/P(antipar) = exp(-E+/T]/ exp[-E-/T] where T is the absolute temperature. Using the fact that the total probability must add up to 1, evaluate the absolute probabilities for the two orientations. Using this show that the average magnetic moment along the field h is m = µ tanh(uh/T) Sketch this as a function of temperature at fixed h. Notice that if h = 0, m vanishes since the moment points up and down with %3D However at any finite temperature, it has a nonzero %3D equal probability. Thus h is the cause of a nonzero m. Calculate the susceptibility, dm lh=0 as a function of T.
Transcribed Image Text:Problem 1.6.5. A magnetic moment µ in a magnetic field h has energy E+ = Fµh when it is parallel (antiparallel) to the field. Its lowest energy state is when it is aligned with h. probabilities for being parallel or antiparallel given by P(par)/P(antipar) = exp(-E+/T]/ exp[-E-/T] where T is the absolute temperature. Using the fact that the total probability must add up to 1, evaluate the absolute probabilities for the two orientations. Using this show that the average magnetic moment along the field h is m = µ tanh(uh/T) Sketch this as a function of temperature at fixed h. Notice that if h = 0, m vanishes since the moment points up and down with %3D However at any finite temperature, it has a nonzero %3D equal probability. Thus h is the cause of a nonzero m. Calculate the susceptibility, dm lh=0 as a function of T.
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