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Assume I have built up a pretty high charge by rubbing the floor or something. I want to understand these situations:

  1. I almost always get shocked when I touch a metal doorknob with my bare hand.

  2. I occasionally get shocked if I touch the wooden door first, then touch the metal doorknob.

  3. I almost never get shocked if I'm holding a metal key, and use that key to touch the doorknob. Sometimes I can even see sparks between the key and the doorknob.

  4. This just happened, and I feel is really weird: I'm holding a metal travel mug (water bottle) full of water. I start pouring the water down to a metal sink. I get shocked exactly when the water hits the sinks.

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Related: physics.stackexchange.com/q/4180/2451 and links therein. –  Qmechanic Dec 3 '12 at 21:33
    
Thanks. I've read a few related questions. People seem to be talking a lot more about "how to avoid being shocked" rather than "why it works". Also, I feel the bottle/water example (#4 in OP) is almost contradicting to existing explanations on why holding a key works. –  user1032613 Dec 3 '12 at 21:42
    
Your key is probably bare metal, perhaps your metal travel mug is painted or lacquered? –  RedGrittyBrick Dec 3 '12 at 23:05
    
@RedGrittyBrick Yes, you are absolutely right about this. Any idea why this is the case? –  user1032613 Dec 4 '12 at 4:38
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@user1032613: I guess your travel-mug is painted as a decorative effect or lacquered to preserve it's shiny finish and prevent corrosion. These layers act as an insulator. You only feel the discharge if it is concentrated in a tiny spot as a spark that leaps across a small air gap from your skin to a conducting surface (e.g. a small scratch in the travel-mug's coating where the underlying metal is exposed, the poured water creates a path to complete the circuit through which the static charge is discharged). –  RedGrittyBrick Dec 4 '12 at 10:07
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2 Answers 2

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When your feet rub the floor you acquire a small electric charge due to the triboelectric effect. The wiki page explains the mechanism:

"After coming into contact, a chemical bond is formed between some parts of the two surfaces, called adhesion, and charges move from one material to the other to equalize their electrochemical potential. This is what creates the net charge imbalance between the objects. When separated, some of the bonded atoms have a tendency to keep extra electrons, and some a tendency to give them away, though the imbalance will be partially destroyed by tunneling or electrical breakdown (usually corona discharge). In addition, some materials may exchange ions of differing mobility, or exchange charged fragments of larger molecules."

When you bring your finger near a conductor, the electrons on the conductor will relocate due to the electric field from your finger. For example, if you are negatively charged then the electrons on the surface of the conductor will move away from your finger, leading to a local positive charge which attracts the electrons on your finger. If the charge on your finger is large enough, and if your finger is close enough to the conductor, the local electric field can overcome the dielectric strength of the air resulting in the partial ionization of the air. The electrical resistance of the air will fall substantially, allowing current to flow quickly between your finger and the conductor. You feel the shock.

If you bring your finger near an insulator like wood, the electrons on the insulator won't relocate like they did on the conductor. The electric field will be smaller and will probably not cause the air to break down. When you touch the insulator, the charge imbalance will (at least partially) neutralize. This will not happen as quickly as with the conductor though because the resistivity of the insulator will not permit as high a current per unit area, so you won't feel a shock. The insulator will acquire a charge in the area you touched.

Since the insulator does not readily permit the flow of charge, it may not fully neutralize your charge imbalance, so when you go on to touch a conductor you may still feel a shock, albeit weaker because some of your charge has been dissipated.

That should cover 1 and 2. For 3, there is still current flowing (which explains the sparks you see) but since the contact area between your fingers and the key is much larger than the approximate cross sectional area of the spark the current per unit area is much smaller and you don't even feel it flow from your fingers, through the key, into the doorknob.

Number 4: without seeing your travel mug I'd say RedGrittyBrick is probably right when he commented "...your travel-mug is painted as a decorative effect or lacquered to preserve it's shiny finish and prevent corrosion. These layers act as an insulator. You only feel the discharge if it is concentrated in a tiny spot as a spark that leaps across a small air gap from your skin to a conducting surface (e.g. a small scratch in the travel-mug's coating where the underlying metal is exposed, the poured water creates a path to complete the circuit through which the static charge is discharged)."

It is worth noting that pure water is a terrible conductor of electricity. The Z-machine uses 2.3 million liters of deionized water as part of its insulation.

Here is a paper exploring the electrical properties of skin. On pg 848 the authors describe skin's current response to rectangular pulses between $5V$ and $60V$. They observe "in this range of voltages the skin behaves as a nonohmic, nonlinear system, with a conductance that increases with increased voltage. At the beginning of a pulse, the current dropped to a minimal value and then slowly increased."

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Thank you very much for your detailed answer. One more follow up: I should have more electrons in my body after rubbing the floor, and they want to get out as soon as I touch some grounded metal, like the doorknob, right? Before touching, those "extra" electrons would be flowing freely in my body. To my understanding, drifting speed is as slow as several mm/s. How do these electrons get to my finger tip to travel to the doorknob so fast? –  user1032613 Dec 6 '12 at 19:51
    
Whether you gain electrons or lose electrons depends on the materials being rubbed together. There is a list on the wiki page for triboelectric effect that organizes materials according to charge separation. Many carpets are nylon which tends to go (+), while synthetic rubber (shoes) tend to go (-), so yes you'd probably end up with an excess of electrons on your body. –  xxx Dec 6 '12 at 20:31
    
I don't think its correct to assume that all of the excess electrons must flow from all over your body, down your arm, then out your finger. The electrostatic repulsion among your excess electrons will help push electrons off your finger, leaving your finger temporarily deficient of electrons relative to the rest of your body, then the charge distribution of your body will adjust to reach a new equilibrium. I'm not sure exactly what's happening though because the electrical properties of skin are complex. I'll add an edit with more info. –  xxx Dec 6 '12 at 20:45
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You are quite right about the origin of the charge. You can build up a very high charge that way. But it doesn't take many electrons to build a high charge.

Now when you touch a conductor (wood should not cause a shock) that charge is discharged by a current running from your body down to your finger. However the actual current is fantastically small. So you get a spark discharge which you can feel as a kind of pinprick and that's that.

This happens mainly in the winter time and in environments with very low humidity. Thick pile rugs and fuzzy car seats are prime offenders. At other times of the year when the humidity is higher, the charge never builds up, leaking away because of the moisture content of the air.

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