Skip to main content

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)

Deaver B. & Fairbank W. (1961). Experimental Evidence for Quantized Flux in Superconducting Cylinders, Physical Review Letters, 7 (2) 43-46. DOI:

2.  Flux trapping on Copasetic Flows

3.  Fairbank and fractional charge

4.  Quantum Hall review article
Yennie D. (1987). Integral quantum Hall effect for nonspecialists, Reviews of Modern Physics, 59 (3) 781-824. DOI:

5.  Fractional quantum Hall effect (open access)

6.  Scientific American on the Quantum Hall Effect

7.  Fairbank apparatus progenitor
Foner S. (1959). Versatile and Sensitive Vibrating-Sample Magnetometer, Review of Scientific Instruments, 30 (7) 548. DOI:


Popular posts from this blog

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 rule can be used to convert a differe…

Division: Distributing the Work

Our unschooling math comes in bits and pieces.  The oldest kid here, seven year-old No. 1 loves math problems, so math moves along pretty fast for her.  Here’s how she arrived at the distributive property recently.  Tldr; it came about only because she needed it.
“Give me a math problem!” No. 1 asked Mom-person.

“OK, what’s 18 divided by 2?  But, you’re going to have to do it as you walk.  You and Dad need to head out.”

And so, No. 1 and I found ourselves headed out on our mini-adventure with a new math problem to discuss.

One looked at the ceiling of the library lost in thought as we walked.  She glanced down at her fingers for a moment.  “Is it six?”

“I don’t know, let’s see,” I hedged.  “What’s two times six?  Is it eighteen?”

One looked at me hopefully heading back into her mental math.

I needed to visit the restroom before we left, so I hurried her calculation along.  “What’s two times five?”

I got a grin, and another look indicating she was thinking about that one.

I flashed eac…

The Javascript Google URL Shortener Client API

I was working with the Google API Javascript Client this week to shorten the URLs of Google static maps generated by my ham radio QSL mapper. The client interface provided by Google is very useful. It took me a while to work through some of the less clear documentation, so I thought I'd add a few notes that would have helped me here. First, you only need to authenticate your application to the url shortener application if you want to track statistics on your shortened urls. If you just want the shortened URL, you don't need to worry about this. The worst part for me was that the smaple code only showed how to get a long url from an already shortened rul. If you follow the doucmentaiotn on the insert method, (the method for getting a shortened url from a long one), there is a reference to a rather nebulous Url resource required argument. It's not at all clear how to create one of these in Javascript. The following example code shows how:
var request = gapi.clie…