See separate entry.

Day 17: Magnetic work

  1. Units: cgs and mksa
  2. Change of internal energy of sample and EM fields
  3. EM has moment density, SM has total moment
  4. Field energy, moment energy, Joule heating
  5. Types of magetism, para, dia, ferro, anti-ferro, ferri
  6. Experimental observations, ordering temperature
Problems in class
  • What are Maxwell's equations?
  • What is the Poynting vector?
  • How can one observe difference between AF and Para?

Students were able to reconstruct Maxwell's equations in about five minutes, working in groups. They all did the differential form, and all used MKSA units, as is done in 431 and 481. These units are better for experimentalists. There were some inconsistencies in using matter or not. They knew about the Poynting vector, which was just done in 481. I derived the energy ablance by enclosing the system by a surface and integrating the Poyning vector over that surface. That gives you the DECREASE of internal energy per time of the system. Than do the same Maxwell stuff, and you see that the change of internal energy is the internal Joule heating (now positive!), the field energy, and the energy of the moments in the field. Experimentally it is hard to exclude the field energy from the system. This avoids making the Joule heating a work term.

Day 18: Paramagnetism

  1. Measuring magnetism
  2. Paramagnets, susceptibility Curie law
  3. Langevin
  4. Two level system
  5. J level system?
  6. Why heat capacity is hard
Problems in class
  • Derive force in field gradient
  • Example of M(H) measurements, what do you need to know?

Class was empty after quantum midterm. We did a warm-up exercise finding the consequences for Maxwell's relations and adding the field energy to the Gibbs like free energy. At constant V no change, but at constant p there is a change because V varies. I mentioned that measuring thermodynamic properties requires using thermodymanic measurements. In our case we need to measure M directly. We can measure M indirectly from NMR or other techniques, but then we need physics to connect the two, and that is potentially dangerous, because it is often that physcis we want to test! Gave them M(H) and got to the explanation in terms of independent moments. Did the Langevin derivation in class, looked that there was a mistake (there was not), and decided to give this as a homework problem for Monday, so everybody had seen it.

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