Say you have an infinite plane of sheet metal. You connect a positive and a negative wire (you know what I mean, don’t nitpick me) say one meter apart from each other and with sufficient power to electrocute you. I don’t think the whole thing becomes a death trap, does it? Would you be able to stand on this plane at some distance from the wires and not be electrocuted?
(come to think of it, maybe standing on it won’t kill you because you are not making ground, right?. Make it then a ceiling that you reach up and touch)
In the Hollywood version, the whole thing becomes “electrified” and if you touch it, these big lightning style arcs go all over you and you die.
In reality, it’s like you suspect. The whole thing doesn’t become a death trap.
What you will end up with are these varying voltages across the surface of the metal. You can touch any two points that are at the same voltage and not get shocked at all. Touch any points where the voltage is different though and current will flow through you. The greater the voltage, the more goes through you (basically - the human body has a fairly complex response to electricity and doesn’t really act like a simple resistor).
The bottom chart on this image shows the type of voltage pattern you’d get from having two wires connected to the plate. Where the lines are closer together you’ve got a steeper voltage gradient. Out away from where the wires connect, the voltage gradient gets much more shallow, which means you’d receive less of a shock if you were standing out there. http://www.lightandmatter.com/html_books/0sn/ch10/figs/twodvmaps.png
One of the implications of this in real life is that swimming pools don’t kill everyone in the pool if someone drops a wire in one end (like it would in a Hollywood movie). If someone dropped a live wire in one end of the pool, you could probably swim around in the other end and not feel anything at all. Once you got within about six feet or so of the wire though you’d start to feel some tingling. Of course, if you can feel tingling, you’ve got more than enough electricity going through you to maybe kill you. It’s not likely to at those levels, but death is a possibility. Then of course if you got even closer, you’d feel greater tingling, then pain, then you’d get enough electricity to guarantee that you’d do yourself some damage.
Another implication in real life is that people standing under a tree can be killed by lightning that hits the tree and goes to ground. Contrary to popular belief, electricity doesn’t take the path of least resistance. It takes all paths. It’s just that more of it flows through the paths of less resistance. When lightning hits the tree and starts spreading out through the ground, you get these voltage gradients, much as you would get on your sheet metal plate. If your feet are far enough apart on these voltage gradients, you can get enough current flowing through you to kill you.
If your metal is a good enough conductor, then there will be almost no voltage difference anywhere on the plate, and the current will almost all just flow through the plate, instead of flowing through you.
there is so much current to be dissipated that that the bolt will split well above the ground. it has just traveled miles through low conducting air, everything that can be a path will be a path.
recommended is having feet together and squatting if caught in the open.
Thanks, everything is much in line with my instinctive thoughts about this. (and the pool example is 50% of what made me ask the question).
What is not according to my instinct is that I intuited the top graph more than the bottom. With current flowing from A to B preferring a straight line and then less so in that iron filings under a magnet pattern. What am I missing?
The other 50% of what made me ask this question is: If I touch both wires with one hand, I should burn my hand but not have a heart attack, right? At least not as I would if I touched each wire with one hand and current had to travel through my chest. Am I anywhere near to reality on this one?
An interesting (to me, anyways) question would be; what do the current magnitude and direction look like ‘within’ the plate at different points? Does one of the graphs posted above show that?
I could see modelling the whole plate as a mesh of little resistors. In the case of an ideal zero-resistance conductor, I am guessing (and would sure like to see) that the elctrons flowed from the negative to positive terminal, but ‘fanned out’ somewhat in between due to the electrons repulsing each other.
And yes, I’m from the school that “current” is electrons flowing from negative to positive.
With iron filings and magnets, you’re seeing them line up along the magnetic field, similar to the electric field in the first image in the linked figure. The second figure is a potential field; voltage is a measure of electric potential. Potential measures the amount of potential energy that is gained by a unit of charge in that field.
Elevation is a measure of gravitational potential, so in a really analogous way you can imagine that the potential field in the figure is a hill, and charge is analogous to mass. When masses fall down hills, they pick up kinetic energy and knock into things, sometimes killing them. Similarly, when electric charges fall down a steep potential ‘hill’, like in the picture, they gain energy and knock around atoms, perhaps inside your body. If those atoms get knocked hard enough, you die.
You can see how this applies you your second question: Basically, the farther the charges fall downhill, the more they hurt. So the further apart your hands or feet are (in a steep enough gradient), the more current you’ll get. You are also right about using two hands. It not only will give you a bigger jolt, but the current will pass through your body instead of just through your hand, burning up vital organs in the process.
Rightly or wrongly, technicians were long taught to work “one-handed” when possible to avoid or reduce current across the chest. At very high voltages, things can get a little counter-intuitive because the ratio between the voltage (and resulting current), as well and breakdown conduction, is large compared to the magnitude required to affect end-plate activation (about 90 mV across a muscle end-plate membrane, 120 mv for cardiac muscle, or milliamps of total thoracic current, IIRC), so relatively minor side-effects can induce potentially fatal arrhythmias.
If we’re assuming a voltage source, isn’t the conductivity of the metal irrelevant to the pattern of voltage on the plate? (It’s relevant, though, to how the pattern will change if a person touches it, but that effect will be small.) For a current source, it’s as you say. A real-life source is somewhere in between, but may approach one or the other ideal.
The most common sources in the real world are roughly voltage sources with an internal resistance. As long as the external load has a resistance much greater than the internal resistance (which it usually will, the way most things are designed), it’ll be close to an ideal voltage source. But a sheet of metal is likely to have a resistance significantly below the internal resistance of the source, in which case it basically acts as a current source.
In other words, when the load is just a piece of metal, very few things still behave as an ideal voltage source.
If you’re assuming an ideal voltage source, the conductivity of the metal is the only determiner of the voltage on the plate. An ideal voltage source connected to a perfect conductor is insoluble, as it’s an improperly modeled system. In practice, a metal is closer to being a perfect conductor than most power sources are to being an ideal voltage source.
This is a common misconception that I think comes from the “electricity takes the path of least resistance” myth. Electricity takes all paths, with proportionally more current flowing through the paths of lesser resistance. You’ll get more current flowing along the direct path between the two wires, but you’ll still get some current going way out to the side and all the way around before coming back to the other wire.
That’s basically true, as long as there’s no other current path (like your feet are touching something conductive).
Electricity kills you in basically one of two ways. Either it screws up your heartbeat or it literally cooks you to death. It takes a surprisingly small amount of current to get your heartbeat out of whack. What happens is that your heart can go into fibrillation, where instead of a nice rhythmic beat your heart is kinda just shaking. Your heart has kind of a weird design that if you can get it into this state it is stable, meaning that it will stay in fibrillation until something gets it out of this state. If someone isn’t standing next to you with a portable defibrillator, you’re in a big heap o’ trouble.
Throwing your heart into fibrillation is kinda hit and miss. Your heart is more sensitive to getting thrown out of whack at certain times in its cycle than others. It’s also kinda funny that moderate shocks are more likely to throw it into fibrillation than both higher and lower level shocks. Lower level shocks have less energy, so that’s no surprise, but higher level shocks tend to make the entire heart contract instead of going into fibrillation. Your heart still isn’t pumping blood, so you’re in a big heap o’ trouble until someone removes the source of the current, but once these higher level currents are removed the heart usually goes back into a normal rhythm.
Of course, once you get too high of a current level, things start cooking. That’s not so hit or miss. Lightning and the electric chair kill you by cooking you to death. It’s like your hand example, though. The path of the current determines what parts get burned, and therefore determines whether you die or maybe just lose a limb. The path of the current in the electric chair is chosen so that it’s not hit or miss at all. People don’t randomly survive “Old Sparky”. The path that lightning takes is much more random, though. At those high voltage levels, things that you don’t normally consider conductive become current paths.
The graph on the lower left has little arrows showing the direction of the current flow. The lines are equipotential lines (any point on the line has the same voltage). The length of the arrow indicates the magnitude of the current at that point.
A slight problem with that graph is that it doesn’t draw the field lines when they get dense. It’s comprehensible if you know the relation of voltage and field strength, though. Here it is in context.
The current pattern will follow the pattern of the field (very strong on the line between the two, with some spreading out as you suspected).
Of course the arrows will point the other way if you use the ‘electron flow’ direction convention. (I’d argue that whichever way you decide to point it, it’s better to refer to current as charge moving rather than electrons. In this case it doesn’t really matter.)
Or, equivalently (by the Norton Theorem), current sources with parallel resistance. That’s what I meant by “somewhere in between”.
That omits any consideration of how far the leads are from each other and how thick the plate is. Placing them far from each other requires long wires, but they may have lower resistance than the plate due to their thickness.
In which case the conductivity of the plate is still the most important element. (I’m using ‘conductivity’ in a technical sense, as a measurable material quantity; it’s not clear whether you meant it in that sense originally.) What determines the pattern of voltage if not that, combined with the other things you mention like distance and thickness of the plate?
Those are the things that determine it, along with the properties of the source. The point is that earlier comments took no account of plate thickness and distance. It makes no sense to say that “a metal is closer to being a perfect conductor than most power sources are to being an ideal voltage source.” Given sufficient distance or a sufficiently thin plate, the resistance will be much larger than the internal resistance of the power source, and it will behave much like an ideal voltage source.
Well, the OP said “sheet metal”, rather than “foil”, and one assumes that he’s talking about a setup of human-scale size. If the metal is thick enough to be called “sheet metal”, and the contacts are only a few meters apart, then the resistance of the metal is going to be very low indeed.
I accept that my statement glossed over the assumptions (which I think were reasonable and Chronos describes well enough). I’m just not sure about your earlier statement that the conductivity of the plate is irrelevant.
Just now I realized that what you may be referring to is that as long as the material’s the same the basic pattern is going to look like the picture engineer_comp_geek posted, regardless of what the conductivity of the metal is. That is true – consider that that graph, in context, is just of two point charges in a plane, without necessarily any current flow at all. To clarify, when I said the conductivity determines the pattern of voltage, I meant how much those values are scaled (I was also allowing for anisotropic materials).
I don’t think that goes against Chronos’s point: The voltage difference between the positive and negative terminal will be next to zero (even though the graph of current and voltage will still look exactly the same). As a practical matter, it’s going to be really hard to come up with a set-up in which any dangerous current will flow through a person standing on the plate, as in the OP.
I imagine you’d need about 1.21 Gigawatts to get there.
OK, equation time. The resistance of an infinite sheet of metal is given by R = rholn(2)/(pit), where rho is the resistivity, ln is the natural log, and t is the thickness (the spacing between the electrodes doesn’t matter, so long as it’s large compared to the thickness). If we assume that the sheet metal is iron or tin (about the highest resistivity metals the OP is likely to be talking about), we have a resistivity of 10[sup]-7[/sup] Ohm-meters. If our sheet metal, in turn, is a mere tenth of a millimeter thick (which is awfully thin to be called “sheet metal”), then we’ll have a total resistance of about 0.2 mOhms (possibly as much as two orders of magnitude less than that, if we use aluminum or copper and make it thicker). Internal resistances of common battery types seem to be in the range of about 10-100 mOhms, and you’d need to string a lot of those in series to get up to dangerous voltages. There might be some other sort of real voltage source with an internal resistance of less than a fraction of a mOhm, but I doubt it. So I stand by the claim that the OP’s sheet metal is a lot closer to being an ideal conductor than the voltage source is to being an ideal voltage source.