# Would Beetee's electrocution plan work and kill the tributes in the lake?

In Catching Fire, the second episode of the Hunger Games trilogy, one of the characters (Beetee) proposes a plan to kill some of the remaining tributes. He proposes wrapping a special wire that he has designed to withstand the vast energy of lightning around a tall tree and running it down to a salt water lake. Then when lightening strikes the tree (which it does predictably every twelve hours) anyone in the lake will be killed. (N.B. This is not Beetee's real plan, but it is the one he wants his allies to believe.)

I don't think his plan would work at all. Assuming that his wire can carry the enormous current delivered by a lightening strike (this is fiction after all) surely the current would short to ground through the salt water rather than taking a path through anyone standing or swimming in the water. The analogy I have in mind is that of birds standing untroubled on live electricity wires. They are unharmed because they do not provide a path to earth. But another analogy might be dropping a mains electric heater into a bath when you are in it. I think that kills you (though I'm not sure why.)

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I asked this on the Electrical Engineering Stack Exchange but the comments suggest it is off-topic there. Hopefully it is on topic here. One comment also suggests that this is a field analysis question so I've added "electric-fields" as a tag (and the lab safety tag is a bit tongue-in-cheek, sorry). –  dumbledad Jan 6 at 15:01
It's an artificial landscape and the Game Masters could make it do whatever they want. Meanwhile, a lightning strike delivers a pulse of high voltage&high current, and that travelling pulse could well go thru anything in the water. –  Carl Witthoft Jan 6 at 15:06
Thanks Carl - would such a pulse go through anything in the water? –  dumbledad Jan 6 at 15:07
If people are in the lake, they are basically conductors, being largely made of salt water, insulated only by a little layer of wet skin. –  Mike Dunlavey Jan 6 at 16:59
Thanks Mike; is it enough that they are conductors or do they need to be better conductors than the salt water around them? My thinking was that the electricity would go to ground through the salt water without spreading throughout the lake and through the conductors therein. –  dumbledad Jan 6 at 17:07

There is a related question on the Skeptics SE. The answers cite a number of press reports about injury to swimmers from lightning, though I don't think it's clear what exactly happened so I wouldn't read too much into it.

Fresh water isn't an especially good conductor of electricity. I don't have figures to hand but i would bet that human flesh is a better conductor of electricity than fresh water because it contains more dissolved electrolyte. So if you managed to build up a significant potential gradient in a body of water it would electrocute someone swimming in the water. How much current would flow, and whether it would be dangerous would be very hard to say. In the case of your wire in a lake I would guess you'd need to be very close to the wire for it to be significant. Specifically you'd need to be nearer the wire than the lake shore otherwise the current would simply flow to shore and then to ground.

So while it's possible, it doesn't seem likely to be an effective way of killing other contestants. I'd just stick pointy things in them instead as that appears to work well.

Response to comment:

I got curious about this, so I decided to do the experiment. Since I'm short of lakes, lightning and sacrificial victims my experiment is rather more modest:

My lake was a plastic bowl, the lightning was a 12V car charger and the electrocutee was a digital voltmeter. I started by measuring the voltage as a function of separation of my probes. The plastic box is 16cm long, so the last data point at 16cm separation is almost the whole length of the box. I did the experiment with fresh water and with 3.5% saline (same salt concentration as sea water).

You get what you'd expect i.e. a linear potential gradient. There's a big voltage drop at the electrode/water interface so the maximum poltential difference is only about 4V. It was also a bit variable when using saline as the electrodes started dissolving due to electrolysis (the scrifices I make for science) I wouldn't read too much into the difference. Saline and pure water are the same within experimental error.

Next I measured the current between the probes as a function of separation:

Be careful with this diagram as there's a factor of about 600 between the two sets of data. The saline gave currents from zero to 120 milliamps while fresh water gave currents of zero to 700 micro amps.

So have I proved you could electrocute someone in a lake with a potential diverted from lightning. Yes(ish). If you draw a circuit diagram representing the various paths current could flow it looks like:

The current has to flow from the wire to reach the victim and there will be a resistance $R_A$. Likewise the current leaving the victim has to flow to earth and there will be another resistance $R_B$. If these resistances are low, as in saline, a large current will flow, which is good for lightning based assasinations. The trouble is that the water around the victim acts as a resistor in parallel with the victim. A very low resistance means a large current, but the current will tend to flow around the victim not through them. Large resistances, as in pure water, will mean a low current but more of it will flow through the victim. In my experiment my ammeter has effectively zero resistance so the current always flows through it.

My guess is that there is an optimum resistivity that is low enough to keep the current fatally high, but but high enough not to divert the current around the victim. But I don't have the data to try and calculate what that might be. However my house in Chester is only a few miles from the sea, and we have been getting thunderstorms recently, so if there are any volunteers I feel another experiment coming on.

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Thanks John; it's worth noting that this is a salt water lake, does that change things or would the current still "simply flow to shore and then to ground"? –  dumbledad Jan 6 at 17:15
@dumbledad: it doesn't really answer your question, but I've extended my answer to include some stuff you might find interesting. –  John Rennie Jan 6 at 19:04
Thanks John. Along similar lines (but no graphs and mains instead of a car battery) Li-aung Yip posted a link to a very scary experiment: youtube.com/watch?v=dcrY59nGxBg –  dumbledad Jan 6 at 19:31