Copasetic Flow

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...