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"It is easy to produce a potential difference of several thousand volts between your body and the floor by scuffing your shoes across a nylon carpet. When you touch a metal doorknob, you get a mild shock. Yet contact with a power line of comparable voltage would probably be fatal. Why is there a difference?"

My response:

Potential is Electric Potential Energy per unit charge; 1000V can either be 1J carried by 1 mC of charge – or 1000J carried by 1C of charge. The discharge of the latter of the two transfers x1000 times the energy of the former. A power line carries a lot more charge than the charge accumulated by scuffing shoes against a nylon carpet; hence, upon discharge, a lot more energy is transferred – which is deadlier.

Accurate? Also, a follow-up question: Which is deadlier - 1000J discharged by 1C of charge, or 1000J discharged by 1 mC of charge?

OverLordGoldDragon
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  • There's a nice sentence: "It's not the Volts that kill you, it's the Amps!" The real answer is a bit more complicated than that as, for instance, if the Potential difference is high, then current may actually "break" your skin (which is an isulant) and get into your bloodflow, where, since there is little resistance, a low current may also be lethals – Massimo Pesavento Jun 17 '17 at 08:03

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As noted in the comments, it's not the voltage you need to be thinking about, but rather the current. To see why, we must delve into some biology.

Your heart is kept beating by a network of nerves that rely on small bursts of electric current to communicate. Lethal electrocution happens when these nerves are interfered with by an external current, which usually leads to cardiac arrest. In order to interfere with nerve communication, the external current must be about as large as the current the nerves already use, which happens to be around a few mA. Hence, when receiving a shock with a current of a few mA, the muscles closest to the shock uncontrollably contract, which may lead to being unable to let go of whatever is shocking you.

Of course, your body has some electrical resistance, which means that for a longer path (like the one needed for current to flow through your heart), typically a bit more external current is required. This is why the figure of 10 mA for lethality is typically given. But this also requires another thing I've been assuming for a while: for electrocution to actually be lethal, it must be applied for at least a few seconds, or else the impulse will not significantly affect nerve functioning.

Now, back to your example. On a charged metal doorknob, the voltage between your hand and the doorknob is normally quite high. Additionally, when you receive the shock, though there is not much charge in motion, it moves extremely quickly, so the current can also be quite high (although it would take some impressive conditions indeed for it to be a significant fraction of an amp). But it only lasts for a few microseconds at most, meaning it fails to be anything more than uncomfortable.

In contrast, the shock from a power line actually does carry significant current, and it does so as long as you're holding onto the line. Since, as I've already mentioned, your muscles have contracted uncontrollably, that will probably be until you're dead.

probably_someone
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  • Thank you for your response. Some follow-ups: (1) I prefer an explanation in terms of charge; for current, use charge / time. (2) Higher voltage means higher J/C - meaning, electrons accelerate more as they travel across the potential gradient, thus have a greater velocity, and pass through a cross-sectional area at a greater rate - hence greater current, correct? (3) Your 'at least a few seconds' is missing a half; a lightning strike may last milliseconds, but may be enough to end someone. Then I infer it's time AND current - or, total charge transferred. – OverLordGoldDragon Jun 17 '17 at 13:29
  • So, then, in discharging a charge accumulated from rubbing against a carpet, there is less charge being transferred, and maybe less current - and it lasts less ('maybe' because at a certain point a potential can transfer only so many electrons through a given path - and I cannot tell unless given the specifics of the system being analyzed). So, via a power line nerves are interfered with more flowing charges, and there are more charges and they last longer - hence, more lethality. Correct? – OverLordGoldDragon Jun 17 '17 at 13:32
  • See, here's the thing - there's no net charge being transferred to you by the power line. Charge is flowing through you, but no charge is actually transferred to your body. So a charge-based description is impossible. – probably_someone Jun 17 '17 at 17:08
  • Current is charge/time by definition. If a charge-based description is impossible, so is a current-based description. – OverLordGoldDragon Jun 17 '17 at 20:00
  • I'm aware it's mostly the existing charge within my body that's oscillating or otherwise behaving differently due to the applied electric field - but it's still charge, and can be described as such. – OverLordGoldDragon Jun 17 '17 at 20:01
  • But why would you want to describe it like that? – probably_someone Jun 17 '17 at 20:10
  • Because to me, the concept of current only makes sense in terms of charge and time; it's like trying to describe velocity without involving distance and time. I need to be able to visualize the situation - how electrons respond to applied electric fields and what consequence this behavior has on the entire system (ex. the human body). Simply saying "there's high current, therefore lethality" doesn't cut it for me. In fact, I don't even understand what's meant by a current in the body - should probably make another thread on that. I don't think my current question needs to go that far, however. – OverLordGoldDragon Jun 17 '17 at 20:15
  • Let's put it like this: you are hurt (possibly dead) if a strong enough current flows through you for a long enough time. I don't know if there is a way to quantify this in a single parameter. The point is that the doorknob has only a limited amount of charge it can provide to the current (or, in other terms) the voltage decreases over time. On the other hand, the power line has an "infinite" supply of charge (constant high voltage). A fast strong current, which dies out over time, or, on the other hand, a huge amount of charge diluted over a long time (small current) will not harm you. – JalfredP Nov 15 '18 at 21:44