Thoughts on Fairbank's Quantized Flux Discovery and the Quantum Hall Effect

William Fairbank might be most famous for experimentally demonstrating that magnetic flux is quantized[1]. In 1961 he published the results of an experiment that exposed very small cylinders of superconducting tin to a magnetic field and then measured the magnetic flux trapped by the cylinder after the applied magnetic field was turned off. For more detail on why the flux was trapped, see [2]. He arrived at the following graph of trapped flux vs. applied field strength. (picture 1)

The data points are clustered around magnetic flux levels on the y axis that correspond to the values predicted for the magnitude of quantized magnetic flux. The apparatus for the experiment is similar in several ways to the apparatus for the fractional charge experiment I mentioned yesterday [3]. A superconductor was exposed to an external magnetic field and results were analyzed by measuring properties of an induced vibration of the superconductor through a magnetometer, (an inductive pickup coil).

Almost three decades later in 1980, Klitzing experimentally verified the quantum Hall effect. This is another effect due to the quantitization of magnetic flux. His data was similar to the following[4]. Notice the naturally similar structure, (both experiments are measuring quanta of magnetic flux). (picture 2)

A few years later in 1997, it was experimentally verified that in a two dimensional electron gas, electrons could behave as quasi-particles with one third the charge of a normal electron. The following data shows a plateau at a flux level corresponding to a charge of 1/3[5]. (picture 3)

My leisure time this week is probably going to wind up being spent wondering if the fractional quantum hall effect had anything to do with the fractional charge results Fairbank reported in 1977[3]. Does anyone happen to know if this has ever been addressed? All thoughts, comments, and/or questions are always welcome!

A final note, Fairbank's constructed his quantized flux apparatus based on a vibrational magnetometer design published in 1959[7]. It's definitely my favorite piece of experimental equipment for the week. The prototype was build from a loudspeaker, a drinking straw and a paper cup! (picture 4)

References:

http://dx.doi.org/10.1103%2FPhysRevLett.7.43
Deaver B. & Fairbank W. (1961). Experimental Evidence for Quantized Flux in Superconducting Cylinders, Physical Review Letters, 7 (2) 43-46. DOI: 10.1103/PhysRevLett.7.43

2. Flux trapping on Copasetic Flows

http://copaseticflow.blogspot.com/2013/04/lenzs-law-induction-and-levitation.html

3. Fairbank and fractional charge

http://copaseticflow.blogspot.com/2013/05/the-strange-story-of-free-fractional.html

4. Quantum Hall review article

http://dx.doi.org/10.1103%2FRevModPhys.59.781
Yennie D. (1987). Integral quantum Hall effect for nonspecialists, Reviews of Modern Physics, 59 (3) 781-824. DOI: 10.1103/RevModPhys.59.781

5. Fractional quantum Hall effect (open access)
http://rmp.aps.org/abstract/RMP/v71/i4/p875_1

6. Scientific American on the Quantum Hall Effect
http://ist-socrates.berkeley.edu/~phylabs/adv/ReprintsPDF/SHE%20Reprints/21-Quantized%20Effect.pdf

7. Fairbank apparatus progenitor
http://dx.doi.org/10.1063%2F1.1716679
Foner S. (1959). Versatile and Sensitive Vibrating-Sample Magnetometer, Review of Scientific Instruments, 30 (7) 548. DOI: 10.1063/1.1716679

The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1. While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero. This is typically explained in the following way. While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare. That doesn't stop us from looking for them though! Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2]. Cabrera was utilizing a loop type of magnetic monopole detector. Its operation is in...

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

Now available as a Kindle ebook for 99 cents ! Get a spiffy ebook, and fund more physics The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems , there seem to be fewer explanations of the procedure for deriving the conversion, so here goes! What do we actually want? To convert the Cartesian nabla to the nabla for another coordinate system, say… cylindrical coordinates. What we’ll need: 1. The Cartesian Nabla: 2. A set of equations relating the Cartesian coordinates to cylindrical coordinates: 3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system: How to do it: Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables. The chain ...

More Cowbell! Record Production using Google Forms and Charts

First, the what : This article shows how to embed a new Google Form into any web page. To demonstrate ths, a chart and form that allow blog readers to control the recording levels of each instrument in Blue Oyster Cult's "(Don't Fear) The Reaper" is used. HTML code from the Google version of the form included on this page is shown and the parts that need to be modified are highlighted. Next, the why : Google recently released an e-mail form feature that allows users of Google Documents to create an e-mail a form that automatically places each user's input into an associated spreadsheet. As it turns out, with a little bit of work, the forms that are created by Google Docs can be embedded into any web page. Now, The Goods: Click on the instrument you want turned up, click the submit button and then refresh the page. Through the magic of Google Forms as soon as you click on submit and refresh this web page, the data chart will update immediately. Turn up the:...

Copasetic Flow

Search This Blog