Copasetic Flow

There's sooo much going on today.  I'm back in the lab again, but I'm also studying for the last little bit of my EM II class.   Here are the EM notes for today.  Hopefully, I'll get a lab book up again in the morning. Looking at the Leinard-Wiechert Potentials.   We'll have a particel mofin along hte path $\vec{r} = \vec{r_o}\left(t\right)$.  There is a quite lengthy explanation of IRFs, but I'll skip that for now and keep careful track of whether or not this comes back to bite me in the butt.  We define $\vec{R}\left(t^\prime\right) = \vec{r} - \vec{r_0}\left(t\right)$ which is the vector from the point charge at time $t^\prime$ to the observatin poitn $\left(\vec{r}, t\right)$.  This gives us a retarded time, $t^\prime$ determined by $t - t^\prime = R\left(t^\prime\right)$, where $R\left(t^\prime\right) = |\vec{R}\left(t^\prime\right)|$.  This makes far more sense if you translate one of the ever present ever invisible $1$s to a c to ge...

Just a few notes on how to proceed on the penultimate homework of the semester. We're to show that the solutions for the 30/60/90 triangular waveguide given in the last homework set will also work for a waveguide that's formed from an equilateral traingle.  The three corners of the equilateral traingle are located at $\left(x,y\right) = \left(0, 0\right)$, $\left(x,y\right) = \left(a, a/\sqrt{3}\right)$, and $\left(x,y\right) = \left(a, -a/\sqrt{3}\right)$. This falls out immediately from last week's homeowrk.  Because the sine function is peiodic in $\pi$ over the domain from $\left(-\infty, \infty\right)$, the solution given last week in terms of sines will still evaluate to zero on the wall that falls at negative $y$. coordites.  The positive $x$ coordinates of the functions will evaluate to 0 on the wall in the same manner they did before???  There's an issue here.  It's products of the $x$ and $y$ sinusoids that all sum to zero.  These will need t...

I was back in the lab this morning.  I’m working on getting the four point measurement to work on the YBCO sample.  In the grand scheme of things, this is low priority, but it’s important to know that we can successfully make these measurements here before we have a large bucket of liquid helium evaporating with a sample inside.  Here’s what the four point probe measurement looked like: There are still no conclusive results.  With any luck this is a consequence of me not being able to interpret the results more than a bad experimental setup.  The table below details the four point probe readings in ohms as the superconductor cools Table of four point readings Time Resistance kohm Comments 0 -0.35444 Negative reading is probably from swapped sense wires. 16 -0.36735 Immediately after nitrogen pour 59 -0.34466 Near minimum 101 ...

Here's today's special relativistic EM question.  Can the Thomas precession be shown to be a special case of the perihelion advance of relativistic elliptical orbits?  Any ideas?  Here's what's going on: We've been deriving the special relativistic  orbit of a charged particles around another fixed charged particle.  At the end of the day, you wind up with a perihelion advance which is a fancy way to say that major axis of the elliptical orbit won't stay put.  It swivels around, (orbits), the charged particle as well.  The advance angle of the major axis winds up being\\ $\delta\phi = 2\pi\left[\left(1 - \dfrac{\kappa^2}{l^2}\right)^{-1/2} - 1\right]$ Which is very, very, similar to the Thomas angle for the spin precession, or gyroscopic precession along a circular orbit at special relativistic speeds:\\ $\delta\phi = 2\pi\left[cosh\left(w\right) - 1\right]$ $= 2\pi\left[\left(1 - \dfrac{v^2}{c^2}\right)^{-1/2} - 1\right]$ In the expression...

This is kind of cool from yesterday's EM notes.  Our professor pointed out that if you calculate the field from a relativistically moving electric charge, you'll always find that it's pointed straight at the point of observation.  Anyone have any idea why?  The argument could certainly be made that if you measure the field from a static charge that it will also be pointing straight at you.  Then, there's also the realization that the Lorentz transformation only affects the E and B fields in a frame that are perpendicular to the frame's tangential velocity.  I'm not sure that's either here or there since the point of observation can be anywhere.  Here's the associated diagram for the curious.

The lab book today was a bit sparse and a bit dry.  This is a bit odd considering I got to play lab yesterday...  You'll see. First, here's an archival video of the presentation I did last Sunday for the TX APS section meeting here in College Station.  I fumble a few times, but the content is all there.  If you have any questions, they are very, very welcome! The second video has some kind of cool stuff in it.  Not stuff that went the way I had hoped mind you, but cool nonetheless.  Here's the deal; we'd hoped to make a spiffy little superconductor visibly quenching video.  The idea was to suspend a superconductor as a pendulum in a magnetic field.  It was hoped that as the field increased, the superconductor would swing away from the pole of the magnet, (it did), and that as the field increased more, the superconductor would quench and fall from it's suspended state, (it didn't).  Our melt-texture growth superconductor from CAN just wo...

 As always, look to the bottom of the post for background on what's going on. Finally, enough of theory and presentations!  I got back to the lab today!  Here’s the apparatus I built/used. NOTE:   As always, look to the bottom of the post for background on what's going on. No, the oscilloscope is not sticking its tongue out, that’s a floppy disc.  Remember those?   The small solenoid is what’s deemed a pickup coil.  It’s the first prototype, of the coil that will be used to measure the actual currents and magnetic fields produced by the can crusher magnet.  It’s exactly what it looks like, six complete turns made from a jumper wire.  The Styrofoam cup is to avoid abusing the small magnet block too much when it’s dropped.   The ‘scope pictured can capture a single waveform.  Here, it’s slowed way down to make a sweep over the course of several seconds.  It’s being used to look at the...