In my second semester physics lab (oh, so many years ago) we did an experiment involving a Helmholtz coil (I don’t remember the nature of the experiement, nor much about second semester physics). There was a plasma stream which got bent into a circle by increasing voltage to the coil. Reading Cecil’s column today, he notes that when charged particles accelerate, they give off radiation. Did that happen here? In what band were photons given off if that is so?
Thanks,
Rob
They did radiate. In this experiment, you basically were making a baby synchrotron, which means that the electrons would be giving off synchrotron radiation during the experiment. Synchrotron radiation is emitted in a broad spectrum, but it’s peaked around 0.2 times the “critical frequency” w[sub]c[/sub]:
w[sub]c[/sub] = (3/2) c/r
where r is the radius of the path of the electrons. This assumes that the electrons aren’t relativistic, which is the case when we do this experiment in the teaching labs at my college. (Their maximum energy is about 500 eV in our labs, which gives a speed of about 1/20 the speed of light — not fast enough for relativity to affect things.)
This means that if your electron path had a radius of about 5 cm, the electrons were radiating most of their energy around a frequency of 2 GHz, give or take an order of magnitude. This is in the microwave band of the spectrum — not energetic enough to cause any concern.
If the electrons are non-relativistic, wouldn’t you get cyclotron radiation, not synchrotron?
Crap, good point. In that case, the fundamental frequency of the orbit is closer to v/r, not c/r, and so the characteristic frequency of the radiated waves will be of that order of magnitude instead. If you’re using a 500-V accelerating potential, the predominant frequency would be on the order of magnitude of 100 MHz, in the radio range. This frequency is also equal to the cyclotron frequency of the electrons, which you could estimate if you knew the strength of the magnetic field you were using.
More correctly, that’s not fast enough for relativistic effects to be large, but they’re always there. In fact, the experiment fundamentally depends on a relativistic effect, namely, magnetism.
You’re probably talking about an experiment to measure the charge to mass ratio of the electron. An electron beam passes through a glass vacuum tube filled with a small amount of Helium or some other gas. The beam (cathode ray) causes the gas to fluouresce, so you can see the path of the beam. When you turn on a magnetic field with the Helmholtz coil, the beam bends in a circle, whose plane is perpendicular to the magnetic field and whose radius of curvature can be used to infer the ratio of the electron charge to the electron mass.