Copasetic Flow

During our math methods lecture yesterday, this pair of formulas came up: Which was very cool because it has the feel of a Fourier series.  It's a sum that approximates a function... The coefficients are line integrals over the contour as opposed to integrals over the conjugate variable.  This is the last in a string of similarities between complex analysis and Fourier analysis that have been building in class lately.  So, it was very cool to find a set of class notes from Dr. Jeffrey Rauch of UMich that directly addresses this: http://www.math.lsa.umich.edu/~rauch/555/laurentfourier.pdf Thanks Dr. Rauch!

It's that time of year again when physics students everywhere are deriving the spherical and cylindrical del, nabla, gradient, or Laplacian operators.  Every derivation I saw prior to this week involved lots of algebra and the chain rule... even mine .  Fortunately for me, a comment on my derivation, and a homework assignment from Rutgers  [pdf] led me to a far simpler and more intuitive way of doing things.  You just start from the differential displacement in a given coordinate system and go from there. The differential displacement in spherical coordinates is: The element in the r direction is easy to understand.  A small displacement along the r direction is represented as dr.  The theta and phi displacements might not be as obvious.  The graphic to the left illustrates what's going on.  With small displacement along the theta direction you're moving along a circle with radius r.  The distance you've moved is equal to the len...

The data taken last week showed a linear dependence between the voltage measured in the pick-up coil when the superconductor is levitated and the frequency of the current driving the levitating electromagnet. While reading an article on a susceptometer for superconductors , I came across the graph shown below that shows the decrease in the magnetic field of a solenoid driven at 5 V rms as frequency is increase.  A solenoid is an inductor with an impedance that is linearly dependent on the frequency of the current flowing through it.  The drop in the magnetic field is a result of of the impedance of the solenoid increasing with increasing frequency and reducing the current trough the coil. I'd like to see if the linear increase in the voltage required to attain levitation is just a result of the increasing impedance of the electromagnet.  My first task was to determine a relationshiop between the pick-up coil voltage and the voltage driving the electrom...

The Copasetic Flows  ham radio practice exams have been updated to include the new extra class question pool.  If you see any issues, please contact me at hcarter333@gmail.com and I'll patch them up as soon as I can. 73 de KD0FNR Hamilton

I was greeted by a hissing liquid nitrogen Dewar when I got to the lab today.  Apparently it's normal Dewar venting, but our last two didn't do this, so it was a bit interesting.  I was able to take more data today and there's a linear trend evolving.  As the frequency of the current driving the electromagnet is increased,the amplitude of the current has to be increased to achieve levitation of the superocnductor.  A picture of theresulting graph is shown below.  The x axis is frequency.  The y axis is the peak voltage detected on the pick-up coil wrapped around the electromagnet. Here's a picture of the modified pick-up coil. It's just three windings around the top of the magnet.

There's all kinds of stuff going on today as I try to get the apparatus ready to go to measure the amplitude of the magnetic field required for levitation at each frequency. First, the levitation detector on the sample holder. Building the levitation detector on the sample holder and the liquid nitrogen reservoir didn't work out nearly as well as I'd hoped that it might.  First you ask, what's a levitation detector?  Up until now, I've been determining the moment of levitation after the experiment by making videos that watch the superconductor as the AC magnetic field is increased.  This was fine until I wanted to know what the magnitude of the voltage seen on the pick-up coil used to detect the levitation magnetic field was at the exact moment the superconductor first levitated.  There were a number of problems with doing this with cameras, the least of which was actually needing two cameras. I came up with a system of attaching a piece of aluminum foil to the...

It gets hot in Las Cruces, and sometimes there's nothing to do for it but take a dip.  That's how I found myself sitting in our horse trough with Junior this weekend cogitating about the new data acquisition system.  I had a glass of McAllen, and Junior had her boat, (at 17 months, she's much too young for McAllen), and a good time was had by all.  The horse trough is left over from when we lived in a Quonset hut.  The building didn't come with a bathtub, but a short trip to the local feed store a few blocks away and we were set.  It was kind of cush, the trough sat near the back door about five paces from the train tracks, so you could sit there and watch the trains go by, (see the video below). That was before our landlord decided the space would make a better art gallery. I digress though!  Back to the data acquisition system and its requirements.  I've come across two articles about the effect of alternating current magnetic fields on supe...