Figure 1.
Variation of saturation magnetisation with temperature for Nickel
. Source. This graph shows what happens when you approach the Curie temperature from below.
The wiki comments:
The Bohr-van Leeuwen theorem, discovered in the 1910s, showed that classical physics theories are unable to account for any form of magnetism, including ferromagnetism. Magnetism is now regarded as a purely quantum mechanical effect. Ferromagnetism arises due to two effects from quantum mechanics: spin and the Pauli exclusion principle.
To understand the graph, first learn/remember the difference between the magnetic B and H field.
The interest of the magnetic hystereses graph is that it serves as an important characterization of a :
  • its area gives you the hysteresis loss of the transformer, which is a major cause of efficiency loss of the component
  • some key points of the curve give important characterizations of the core/material:
This curve will also tell you how many turns of the coil will be needed to reach the required field.
Figure 1.
Theoretical magnetic hysteresis plot
. Source.
Video 1.
Measurement of B-H characteristic
. Source.
1989. 1989 and they were making such awesome materials. It is hard to understand why university still exists given this.
Shows how you can obtain the magnetic hystereses curve with an AC source plus an oscilloscope in XY mode. clearly shows the measurement circuit.
Video 2.
Magnetic hystereses experiment by UNSW Physics.
. Source.
2020, thanks COVID-19. Like other UNSW Physics YouTube channel videos, the experimental setup could be made clearer with diagrams.
But this video does have one merit: it shows that the hysteresis plot can be obtained directly with the oscilloscope XY mode by using an AC source. The Y axis is just a measure of the total magnetic field induced by the primary coil + the magnetization of the material itself.
Electromagnets allow us to create controllable magnetic fields, i.e.: they act as magnets that we can turn on and off as we please but controlling an input voltage.
Compare them to permanent magnet: on a magnet, you always have a fixed generated magnetic field. But with an electromagnet you can control the field, and even turn it off entirely.
This type of "useful looking thing that can be controlled by a voltage" tends to be of huge importance in electrical engineering, the transistor being another example.
Solenoids are a type of electromagnet coil of helical shape.
Solenoid means "tubular" in Greek.
Solenoids are simpler to build as they don't require insulated wire as in modern electrical cable because as the electromagnetic coils don't touch one another.
As such it is perhaps the reason why some early electromagnetism experiments were carried out with solenoids, which André-Marie Ampère named in 1823.
But the downside of this is that the magnetic field they can generate is less strong.
Figure 1.
Illustration of a solenoid
Figure 2.
Magnetic field lines around a solenoid cross-section
. TODO accurate simulation or not?
Video 1.
Easy-to-Build Electromagnet lifts over 50 lbs by Dorian McIntire
. Source. Fun, but zero reproducibility.
Video 1.
Yeah, bitch! Magnets! scene from Breaking Bad
. Source.
Video 2.
Police evidence magnet scene from Breaking Bad
. Source.
Toy model of matter that exhibits phase transition in dimension 2 and greater. It does not provide numerically exact results by itself, but can serve as a tool to theorize existing and new phase transitions.
Each point in the lattice has two possible states: TODO insert image.
As mentioned at: some systems which can be seen as modelled by it include:
  • the spins direction (up or down) of atoms in a magnet, which can undergo phase transitions depending on temperature as that characterized by the Curie temperature and an externally applied magnetic field
    Neighboring spins like to align, which lowers the total system energy.
  • the type of atom at a lattice point in a 2-metal alloy, e.g. Fe-C (e.g. steel). TODO: intuition for the neighbour interaction? What likes to be with what? And aren't different phases in different crystal structures?
Also has some funky relations to renormalization TODO.
TODO what it means to solve an Ising model in general? gives some good notions:
  • is the expectation value of the value. It is therefore a number between -1.0 an and 1.0, -1.0 means everything is always down, 0.0 means half up half down, and 1.0 means all up
  • : correlation between neighboring states. TODO.
A tiny idealized magnet! It is a very good model if you have a small strong magnet interacting with objects that are far away, notably other magnetic dipoles or a constant magnetic field.
The cool thing about this model is that we have simple explicit formulas for the magnetic field it produces, and for how this little magnet is affected by a magnetic field or by another magnetic dipole.
This is the perfect model for electron spin, but it can also be representative of macroscopic systems in the right circumstances.
The intuition for the name is likely that "dipole" means "both poles are on the same spot".
Figure 1.
Different macroscopic magnets can be approximated by a magnetic dipole when shrunk seen from far away
. Source.
Applications: produce high magnetic fields for
As of the early 2020s, superconducting magnets predominantly use low temperature superconductors Nb-Ti and Nb-Sn, see also most important superconductor materials, but there were efforts underway to create practical high-temperature superconductor-based magnets as well: Section "High temperature superconductor superconducting magnet".
Wikipedia has done well for once:
The current to the coil windings is provided by a high current, very low voltage DC power supply, since in steady state the only voltage across the magnet is due to the resistance of the feeder wires. Any change to the current through the magnet must be done very slowly, first because electrically the magnet is a large inductor and an abrupt current change will result in a large voltage spike across the windings, and more importantly because fast changes in current can cause eddy currents and mechanical stresses in the windings that can precipitate a quench (see below). So the power supply is usually microprocessor-controlled, programmed to accomplish current changes gradually, in gentle ramps. It usually takes several minutes to energize or de-energize a laboratory-sized magnet.
They are pioneers in making superconducting magnets, physicist from the university taking obsolte equipment from the uni to his garage and making a startup kind of situation. This was particularly notable for this time and place.
They became a major supplier for Magnetic resonance imaging applications.
Used to explain the black-body radiation experiment.
The Quantum Story by Jim Baggott (2011) page 9 mentions that Planck apparently immediately recognized that Planck constant was a new fundamental physical constant, and could have potential applications in the definition of the system of units (TODO where was that published):
Planck wrote that the constants offered: 'the possibility of establishing units of length, mass, time and temperature which are independent of specific bodies or materials and which necessarily maintain their meaning for all time and for all civilizations, even those which are extraterrestrial and nonhuman, constants which therefore can be called "fundamental physical units of measurement".'
This was a visionary insight, and was finally realized in the 2019 redefinition of the SI base units.
Video 1.
Quantum Mechanics 2 - Photons by ViaScience (2012)
. Source. Contains a good explanation of how discretization + energy increases with frequency explains the black-body radiation experiment curve: you need more and more energy for small wavelengths, each time higher above the average energy available.
Derived from classical first principles, matches Planck's law for low frequencies, but diverges at higher frequencies.
  • The Quantum Story by Jim Baggott (2011) page 10 mentions:
    Early examples of such cavities included rather expensive closed cylinders made from porcelain and platinum.
    and the footnote comments:
    The study of cavity radiation was not just about establishing theoretical principles, however. It was also of interest to the German Bureau of Standards as a reference for rating electric lamps.
  • 1859-60 Gustav Kirchhoff demonstrated that the ratio of emitted to absorbed energy depends only on the frequency of the radiation and the temperature inside the cavity
  • 1896 Wien approximation seems to explain existing curves well
  • 1900 expriments by Otto Lummer and Ernst Pringsheim show Wien approximation is bad for lower frequencies
  • 1900-10-07 Heinrich Rubens visits Planck in Planck's villa in the Berlin suburb of Grünewald and informs him about new experimental he and Ferdinand Kurlbaum obtained, still showing that Wien approximation is bad
  • 1900 Planck's law matches Lummer and Pringsheim's experiments well. Planck forced to make the "desperate" postulate that energy is exchanged in quantized lumps. Not clear that light itself is quantized however, he thinks it might be something to do with allowed vibration modes of the atoms of the cavity rather.
  • 1900 Rayleigh-Jeans law derived from classical first principles matches Planck's law for low frequencies, but diverges at higher frequencies.
Video 1.
Black-body Radiation Experiment by sciencesolution (2008)
. Source. A modern version of the experiment with a PASCO scientific EX-9920 setup.
Video 1.
What is the Ultraviolet Catastrophe? by Physics Explained (2020)
. Source.
Video 1.
Time-Correlated Single Photon Counting (TCSPC) with the Fluorolog Fluorimeter by Yale CBIC (2011)
. Source.
One important quantum mechanics experiment, which using quantum effects explain the dependency of specific heat capacity on temperature, an effect which is not present in the Dulong-Petit law.
This is the solid-state analogue to the black-body radiation problem. It is also therefore a quantum mechanics-specific phenomenon.
Observation that all solids appear to have the same constant heat capacity per mole.
It can be seen as the limit case of an Einstein solid at high temperatures. At lower temperatures, the heat capacity depends on temperature.
Wikipedia mentions that it is completely analogous to Planck's law, since both are

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