The method of images

I’ve got a decent idea for a (mathematically) substantial blog post saved up, but this week’s not looking too good work-wise, so you’ll have to settle for pretty pictures instead: 

shake-pole-pdibdin.jpg 

You’re looking at an installation piece by Richard Box consisting of fluorescent tubes powered solely by the potential difference between ground and the top of the tubes (~1.5 meters) set up by the overhead high-voltage lines. Honestly, when I saw this on Gizmodo the first thought through my mind was that I wished I was TAing E&M this semester… 

What’s really interesting is that there should be more going on here than the standard boundary-value problem: ordinary fluorescent tubes have negative resistance (more gas is ionized means more current flows means more gas is ionized…) so a resistive or reactive ballast is needed to regulate the current flow — this is why it’s so hard to make small compact fluorescent bulbs. So for the tubes to stay lit, the resistance of the path through the surrounding atmosphere between the ends of the tube must be in a pretty specific range… unless I’m missing something. Like I said, this is the quickie fill-in post.  

Anyway, as long as we’re at the intersection of boundary value problems and installation art, I can’t resist mentioning The Lightning Field, by Walter De Maria, which made the cover of a really good book about American art… the physics is from the same chapter of Jackson (no relation, by the way, unfortunately) but here we have a field of sharp metal spikes intended to attract lightning via corona discharge.  Apparently, though, this doesn’t work as well in practice… no prizes for guessing how to change the geometry to help.  

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One response to “The method of images

  1. The negative resistance thing isn’t a problem in this context. In a circuit without ballast, these things would draw all the available current and fry, but there simply isn’t enough available here to be a problem. My guess is that at such high frequencies, you could approximate the air as being a perfect capacitor above, and a resistor on the sides. Its 65% humidity in Bath/Bristol right now. I wonder if this would work in lower humidities as well, ie if the capacitance above drops.

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