Gas station without pumps

2012 November 27

Magnetic fields with no lab

Last week we did measurements of the magnetic field around a single wire, and I had planned to “do a lab winding a helix of wire and measuring the field around it.  We’ll use the computational problem (18P79) to compute the expected field in different places, and try measuring the wound solenoid in corresponding locations.  This means that in setting up the program we’ll have to make the number of turns, the radius of the solenoid, its length, and the current through the solenoid all easily changed, to match the simulation to the coil that we wind.”

As it turned out, my son had the simulation finished and we spent most of an hour exploring what the program told us.  The initial picture showing magnetic field arrows near the coil looked fine, but I suggested trying a different visualization: having a particle trace out a magnetic field line.  We expected to see something like the classic pictures of iron filings around a bar magnet, and were surprised to see the magnetic field coiling out from the end of the solenoid.

We did a bunch of debugging.  We looked at at the contributions to the field from the different segments of the coil, by color coding arrows from a fixed observation position. The simulation had n segments for each turn of the helix, so we summed the segments mod n, to get the different contributions from the different parts of the helix.  We also tried varying the number of turns of the helix, and we played with the step size for the particle tracing out the field line.

We finally got some very nice drawings of the field lines coming out one end of the solenoid, spiraling out, then spiraling back in to the other end, and running through the center of the solenoid.  It took us a while to realize that the behavior was indeed what we should have been expecting, because the helix has current running parallel to the axis of the helix as well as around the helix.  A simulation (as the book suggests) using only circular rings would not have included this longitudinal current, and we would have missed some interesting views of the magnetic field.

I’m wondering whether we could have gotten a similar result by superimposing two fields: one computed from a stack of circular rings and the other from a wire down the axis, both with the same current.  I might try writing a program that compares the two approaches.

Because we spent an hour doing simulations and looking at the results, we did not get around to doing homework comparisons (a good thing, since I haven’t done the homework yet) nor did we get around to winding a coil and measuring the magnetic field, which I still want us to do.

2012 April 25

Photoeletric effect

Filed under: home school — gasstationwithoutpumps @ 16:30
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Brain Frank has just posted an exploratory exercise on his blog Teach. Brian. Teach.: Photoeletric Effect.  This exercise relies on a simulation from the University of Colorado at Boulder.

The simulation is of a standard phototube experiment.  A phototube is a vacuum tube diode, in which the cathode is illuminated by a light source.  The photons excite electrons in the cathode, raising some of them to high enough energy levels to become unbound from the atoms and leave the cathode.  The electric field accelerates them toward the anode (or repels them, if the diode is biased backward).  The energy of the electrons is basically the energy of the photons minus the energy needed to raise the electrons from the ground state to the unbound state.  (At very high illumination levels, you can have one photon exciting the electron out of the ground state and another raising it to the unbound state, but I don’t think that effect is being simulated.)

At forward voltages, the current is determined by the illumination, independent of the bias—essentially all the released electrons go to the anode. At reverse biases, only the higher energy electrons have enough speed to make it to the anode. The energy of the highest-energy electrons can be estimated from the reverse-bias voltage at which the current drops to zero.

The simulation seems pretty good, but I don’t know exactly what effects they are modeling.  For the zinc target with high forward bias, there is a current peak around 135 nm, but from the spectral lines at NIST, I would have expected a peak around  127 nm.  I don’t know if the problem is a limitation of the simulation or a limitation of my understanding.

I know that my understanding of quantum effects is very limited, and the simplistic view of the photoelectric effect given in Wikipedia does not cover some of the phenomena being simulated here.  But since I don’t know exactly what phenomena are being simulated, I have no way of predicting the behavior.

I find it frustrating to do the sort of discovery experiment that Brian is proposing using a simulation.  If I knew precisely what was being simulated, there would not be much discovery, but trying to reverse engineer a simulation from its behavior seems to me a rather irritating and frustrating exercise. I not only have to guess at what physics is important, I also have to guess at what physics the writer of the simulator thought was worth including, and what simplifying assumptions he made.  (For example, is the simulation including the absorption of the glass or quartz tube holding the vacuum?)

I suppose I could read the source code (PhET provides that) or read the 17 “Teaching ideas” on the web page for the simulation. The teaching ideas look like a wide range of different lesson plans for labs, demos, and homework questions.  I looked at one of the “advanced” ones, but it seemed to only use the Wikipedia-level model, which does not explain a drop in current with shorter wavelengths.

I’d much rather have real experiments than simulated ones—even if the crudeness of my measurement tools limits the quality of the data I can collect.  The value of simulations is more in writing them and seeing that they predict the behavior you observe than in running someone else’s black-box model.

2012 April 11

Physics simulations

Filed under: home school — gasstationwithoutpumps @ 21:46
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Someone recently pointed me to these Physics Simulations using the free gemoetry/algebra tool Geogebra.  It seems that Geogebra is a pretty good tool for creating 2D geometric drawings that can be animated, though I’ve not tried doing so myself. I don’t have a lot of use in the home-school physics teaching I’m doing for demo programs, and most of the Geogebra programs in this set are for optics or electromagnetism, and so part of next year’s course.

I wonder how Geogebra compares to Vpython for student-written physics programs, though.  Vpython is fairly simple to code (though I wish that it was integrated with Unum, so that all computations could be done with units—having to throw away the units for communicating with Vpython makes carrying around the units almost more trouble than they’re worth.

I had thought that we would do a lot of simulations of physical phenomena this year as part of the Physics C: Mechanics class, but it has not worked out that way.  The students (including me) often did not do the assigned computational problems.  Some of programs were useful, like the pendulum without the small-angle approximation, but a lot just simulated phenomena that were rather obvious from the formulæ, and so were not worth the trouble to write.  I had hoped for more examples like the pendulum, where simulation provided insight that was not available from analytic solutions.

Perhaps next year, when we do the Electricity and Magnetism half of the physics course, there will be more simulations worth doing.

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