A friend and I have been discussing the danger of static electricity causing fires at gas stations. I told him that, in dry air, a 1 cm spark equates to 30,000 Volts. He was quite surprised at this, and asked,

But what I don't understand is how you could ever equalize a potential difference of several thousand volts instantaneously without getting cooked. I've experienced many static electric discharges in my life, as I'm sure nearly everyone has, and yet I'm still alive to talk about it.
Having nothing much better to do, I decided to write him a little explanatory essay. When I was finished, I realized it might be of interest in the context of Everything as well, so here it is. I'm an adult and don't get homework assignments other than the ones I give myself; consider this as noding my homework.

Physical Science pedants may object to my gross simplification of some matters, and my wild-guess estimates. Please consider that this is an explanation aimed at laypeople. Scientists already know this stuff anyway.

If you're still a bachelor, you may consider looking into a book I recently saw advertised on Slashdot: "I'm only here for the food: Food + Heat = Cooking". This is a cookbook which explains the chemical and physical background; a cookbook for geeks. Along the lines of its title, "human limb + energy = cooking".

To cook something means to raise its temperature, and possibly keep it there for a while. This doesn't just take voltage, nor even power: it takes ENERGY. One popular way to measure energy is the calorie, which is defined as the amount of energy required to heat one gram of water one degree Celsius. So here's another formula:

energy / (weight of substance to be cooked) = temperature increase
If I put a cup of water in my 800W microwave for one minute, its temperature goes from about 20°C to 80°C. If I did that with my hand, it would surely be cooked. Here's a couple more formulae:
current * voltage = power
and
power * time = energy
So let's say that to (thoroughly) cook a hand (+ part forearm) requires something on the order of 800W * 60 seconds = 48,000 Watt-seconds.

Now let's look at a static zap: You've wrested enough electrons from a grounded object that you have a charge of some billions or trillions of excess electrons (I don't know the exact numbers, it doesn't matter). The potential difference between you and the ground actually increases in proportion to your distance from it - you can raise the voltage of your charge (relative to some object) simply by moving away. This would require work, because your charge actually pulls you toward the other charge somewhat. Anthropomorphized, a voltage is the yearning of a bunch of electrons to go where they'll even out a charge, and if separated and isolated, they will constantly pull toward where they want to go, and the yearning will increase with distance. Even a single electron can be a kilovolt, if you take it far enough. Again, I won't bother trying to calculate just how far.

Now then... the electrical resistance of your body (mostly skin resistance, because it's pretty moist and conductive on the inside) is measurable with an ohmmeter. This can vary wildly, but let's say it's 100 kiloohms. But in order for there to be a spark, there must also be air between you and whatever. Air is a bad conductor, even when ionized by the spark. Let's guess that we have 10 MOhms (= 10,000,000 Ohms, or a hundred times as much as your hand) of resistance there.

Current = Voltage / Resistance = 20 kv / (10,000,000 + 100,000) Ohm = 0.002 Amps.
Think of this as a flow of 2 gazillion electrons marching through your hand; electrical people call it 2 milliamps. This is enough current to be felt by your nerves. Upward of around 5 to 10 milliamps, it would be enough to make your muscles twitch.

Current moves through a resistance if there's a voltage. Because there are two resistances, the voltage is shared between your hand and the air gap. Turning the above formula around a bit, we have:

0.002 Amps * 100,000 Ohms = 200 Volts
inside your body and the rest (most of the 20,000 Volts) across that air gap. So actually, most of the power of the discharge is heating up the air, not you. Now we can estimate how much power is cooking you:
Power = Current * Voltage = 0.002 A * 200 V = 40 W.
You can get an idea of how much power 40 W is by putting your hand over a 40 W light bulb (don't touch the metal parts!) that's just been turned on: you'll eventually burn your hand on it, but you have plenty of time to pull away before you're hurt. Thus, a steady power equal to that from the spark would eventually cause some burning.

The "secret" of static electricity, though, is that there is no steady supply. Static electricity is a stored quantity of electricity without a backup supply to keep it coming. Those few trillion electrons you ripped off are just a drop in the bucket, energy-wise, and once they jump off your finger and into your car, they're gone, the potential difference is used up and goes back to 0 Volts. A spark crosses over in a very small fraction of a second, so it's able to deliver enough power to sting a very small patch of skin (mostly by direct nerve stimulation) but not to burn anything. Actually, the greater amount of energy released to the air is sometimes enough to ignite a small amount of gasoline vapor, which is where the problem at gas stations comes from.

Another way to look at it: 800W, the power of my microwave, happens to be just a little over one horsepower. So the amount of energy required to cook your arm is about one horsepower-minute. Now a static charge doesn't come from nowhere, energy must be expended in order to build up a charge. Assuming you had a very efficient and lossless static electricity generator, you'd have to exert truly athletic power for a full minute to work up enough energy to cook your arm. Contrast this with the amount of energy that goes into taking a couple of shuffling steps over a carpet, or sliding off a car seat, and you'll understand that there can never be THAT kind of energy in a static charge that's built up by a casual motion of your body.

Good thing, too!

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