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It's been happening to me for years. I finally decided to ask users who are better with "practical physics" when I was told that my experience – that I am going to describe momentarily – prove that I am a diviner, a psychic, a "sensibil" as we call it. The right explanation clearly needs some electrodynamics although it's "everyday electrodynamics" and theoretical physicists are not trained to quickly answer such questions although each of us has probably solved many exercises that depend on the same principles.

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When I am biking under the power lines – which probably have a high voltage in them – I feel a clear tingling shocks near my buttocks and related parts of the body for a second or so when I am under a critical point of the power lines. It is a strong feeling, not a marginal one: it feels like a dozen of ants that are stinging me at the same moment. It seems almost clear that some currents are running through my skins at 50 Hz. I would like to know the estimate (and calculation or justification) of the voltage, currents etc. that are going through my skin and some comparison with the shock one gets when he touches the power outlet.

Now,

  • my bike that makes this effect particularly strong is a mountain bike, Merida;

  • the speed is about 20 km/h and the velocity is perpendicular to the direction of the current in the power line;

  • the seat has a hole in it and there is some metal – probably a conducting one – just a few centimeters away from the center of my buttocks. It's plausible that I am in touch with the metal – or near touch;

  • my skin is kind of sweating during these events and the liquid isn't pure water so it's probably much more conductive than pure water;

  • the temperature was 22 °C today, the humidity around 35%, clear skies, 10 km/h wind;

  • the power lines may be between 22 kV and 1 MV and at 50 Hz, the altitude is tens of meters but I don't really know exactly.

What kind of approximation for the electromagnetic waves are relevant? What is the strength? How high currents one needs?

Does one need some amplification from interference etc. (special places) to make the effect detectable? (I only remember experiencing this effect at two places around Pilsen; the most frequent place where I feel it is near Druztová, Greater Pilsen, Czechia.)

Is the motion of the wheels or even its frequency important? Is there some resonance?

Does the hole in the seat and the metal play any role? Just if you think that I am crazy, other people are experience the effect (although with different body parts), see e.g. here and here. This PDF file seems to suggest that the metals and electromagnetic induction is essential for the effect but the presentation looks neither particularly comprehensive nor impartial enough.

An extra blog discussion on this topic is here:

http://motls.blogspot.com/2012/05/electric-shocks-under-high-voltage.html

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What do you mean " the velocity is perpendicular to the current"? That you are crossing the line under the high tension line? Up to that point I thought you were biking in parallel. –  anna v May 27 '12 at 4:40
    
Had this happened to me, I would have a) taken a small lamp, of the kind used in torches, and made a circuit from a metal part to my insulated hand and watched whether there was light when crossing. If yes, I would take my voltmeter on AC index and watch again between the metal part and my body to measure the current. If no light or current was seen I would presume that the effect was on the physiology of my body ( water mainly) and read up on that. Too many unknown parameters in the problem and it has to be sliced down. –  anna v May 27 '12 at 4:46
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p.s. does the effect stop if you stop at that point? –  anna v May 27 '12 at 5:01
    
Have a look at this stopgeek.com/richard-boxs-light-field.html . also youtube.com/watch?v=cXhZvyGtMrk –  anna v May 27 '12 at 7:37
    
Yes, Anna, it appears when I am crossing but I suspect that if I were riding in parallel on the right place, it could be the same effect. And maybe not. Maybe there's some current running around the bike and the polarizations matter. ... I should make an experiment, like stopping at that point. But it has happened to me about 5 times in my life - although it's pretty safely guaranteed and regular with that bike - and it's unpleasant enough a feeling that I just don't want to repeat it again! But maybe i will do the sacrifice at some point haha. –  Luboš Motl May 27 '12 at 18:08
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7 Answers 7

up vote 17 down vote accepted

First, Field strength.

This calculation is strictly an electric potential calculation; radiation and induction are safely ignored at 50Hz.*

For a 200kV transmission line 20m above ground, the max electric field at ground level is about 1.2 kV/m. This number is reduced from the naive 200kV/20m=10 kV/m calculation by two effects:

1) The ~1/r variation in the electric field (reduction to 3 kV/m). I used the method of images to calculate this field, with a 10 cm conductor diameter to keep the peak field below the 1MV/m breakdown field.

2) Cancellation from the other two power lines in this 3-phase system, which are at +/-120 degree electrical phases with respect to the first, and are physically offset in a horizontal line per the photo. I estimated 7m spacings between adjacent lines. The maximum E-field actually occurs roughly twice as far out as the outermost line; the field under the center conductor is lower.

Next, Can you feel it?

1) The human body circuit model for electrostatic discharge is 100pF+1.5kohm; that's a gross simplification but better than nothing. If one imagined a 2m high network, the applied voltage results in a 50Hz current of about 70uA ($C \omega V$). Very small.

2) There will be an AC voltage difference between the (insulated) human and (insulated) bicycle. A 1m vertical separation between their centers of gravity would yield roughly 1200V. This voltage is rather small compared to some car-door-type static discharges, but it would still be sufficient to break down a short air gap (but not a couple cm), and would repeat at 100Hz. I imagine it would be noticeable in a sensitive part of the anatomy.

If the transmission voltage is actually 400 kV, all the field strengths and voltages would of course double.


(*) In response to a comment, here's an estimate of the neglected induction and radiation effects, courtesy of Maxwell 4 and 3:

Induction: Suppose a power line is carrying a healthy 1000A AC current (f=50 Hz). Then by Ampere's law, there is a circumferential AC magnetic field; at the wire-to-ground distance of 20 meters that field's amplitude is $10 \mu T$. (Compare with the earth's DC field of approximately 0.5 gauss, or $50 \mu T$.)

The flux of this magnetic field through a $1 m^2$ area loop (with normal parallel to the ground and perpendicular to the wire) is $\Phi = 10 \mu Wb$ AC. Then from Faraday's law, the voltage around the loop is $d \Phi /dt = 2 \pi f \Phi = 3 mV$ (millivolts). So much for induction.

One can also estimate the magnetic field resulting from the $1200 V/m$ ground-level AC electric field, which has an electric flux density $D =\epsilon_0 E = 10.6 nC/m^2$ and a displacement current density $\partial D / \partial t = 2 \pi f D = 3.3 \mu A/m^2$. The flux of this field through a $1 m$ square loop (parallel to the ground) is $3.3 \mu A$, so the average magnetic field around the square is $0.8 \mu A/m$, for a ridiculously small magnetic flux density of $1 pT$.

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Excellent, you got a +1 already for your first sentence, a very useful first step... Can a millimeter air gap be replaced by a centimeter of slightly wet shorts? Or is the air gap needed literally, i.e. in between body hair? I am still not getting why 700 V is safe. Why is it unsafe to touch 230 V or 120 V power outlets then? –  Luboš Motl May 28 '12 at 8:15
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@Luboš Motl, 1) With a closed circuit (bridged by an ionic conductive liquid), you get continuous current, which I don't think would be as noticeable as a sudden spark across an air gap. 2) The difference from a power outlet is the energy (or current, or power) available. Again a gross simplification, but the 100pF human capacitor will only supply 10mW under these conditions, while, once current from a wall outlet has started to flow, it will supply $>10A$. I think about 10mA continuously along the right path through the body can be fatal. –  Art Brown May 28 '12 at 17:06
    
Oh, I see, so it's really about a finite charge in a "capacitor" that limits how much I can get out of it... Thanks. I will actually vote your answer as the "real answer to my question" although there have obviously been many other, sometimes even relevant ideas here... –  Luboš Motl May 28 '12 at 17:31
    
@Luboš Motl, Thanks, but I'm frankly puzzled about the actual sensation. I believe you feel it, but am not sure my answer is sufficient to explain it. Maybe someone else will have an idea... I found an error in my superposition of the other phases that raises the field strength to 800 V/m, and will update the answer accordingly. –  Art Brown May 28 '12 at 17:37
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@ArtBrown besides discharges there's another little-known effect: variation in friction of moving charged surfaces. This phenomenon was used in the Marconi era as a radio detector: a sort of motorized sliding capacitor drum. If pants and bicycle seat are sliding, and if metal in the seat+bike has significant AC volts relative to the human body, then a 2F (100Hz) vibration would be felt whenever the surfaces were sliding across each other. Test: does the odd sensation always vanish when gliding below the power lines wo/pedaling? –  wbeaty Jul 5 '13 at 9:17
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If the power line is 20m high, and has the voltage of 1MV , then the electric field (near ground), very roughly, is on order of 1000/30 kv ~ 30 000 v/m (the numbers are very approximate and the field is complicated because it is a wire near a plate scenario, and wire diameter is unknown but not too small else the air would break down, i.e. spark over, near the wire).

You get charged to several tens kilovolts relatively to bike, then you discharge through clothing, again and again, if the line is AC because the voltage is alternating, if the line is DC because as you're moving the field changes magnitude.

The fluorescent lights light up under power lines; the field is this strong.

http://www.doobybrain.com/2008/02/03/electromagnetic-fields-cause-fluorescent-bulbs-to-glow/

With regards to the current, as the current is pulsed (you get charged then rapidly discharge through the air gap), the current can be strong enough to be felt even if average current is extremely small. The pulse current is same as when you get zapped taking off clothing, or the like.

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Right, thanks, +1, exactly, those 30 kV per meter which is huge even if one only gets a small remnant of it is something I am thinking about. Surprising that not too many people get killed in various situations under the power lines... –  Luboš Motl May 27 '12 at 19:31
    
@LubošMotl Hi Lubos. I think that just kilovolts are not enough to kill you, there has to be enough current. I suspect that the 1/r^2 drop of radiated power is enough to avoid deadly currents, it must be the reason the lines are so high. –  anna v May 27 '12 at 20:34
    
+1 Yes, this is the correct answer: eta.co.uk/2010/11/29/… –  John McVirgo May 27 '12 at 20:41
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Luboš Motl: There would not be enough zap. The physiological zap is a complicated function of pulse duration, current, and voltage. In this scenario the total charge that goes through the body on each zap is no bigger than if you get zapped taking off a sweater or stroking a cat (which can also generate several kilovolts), and the pulse duration is so short and energy so low that neither the current nor the voltage are relevant, but the total charge (integral of current by time). –  Dmytry May 27 '12 at 21:41
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When calculating the volts per meter of the static field, it's important to assume that the bicycle is conductive (presumably an aluminum frame).

Without the bicyclist, one would use image charges to calculate the electric field at the bicycle. The three phases should partially cancel, and Art Brown's calculation seems reasonable, around 1200 volts per meter.

By the way, there's an additional DC voltage; the atmosphere (on a fair weather day) carries a voltage of about 60 to 100 volts in summer and 300 to 500 volts per meter in winter. On days when this effect is large it may be possible to see more of an effect.

When you insert a vertical conductor into the electric field of 1200 volts per meter, the electric field near the ends of the conductor are much larger. To estimate the effect you need to guess the radius of the top end of the conductor. This depends on the seat construction; if the seat itself is metal then its radius is on the order of 0.1 meter.

To first order, a vertical pole placed in an electric field will end up with charges at its two ends. For a bicycle frame of height 1m, the charges will be separated by about 1m. Of course the charge required to cancel the background potential depends on the radii of the ends of the pole. (An infinitely sharp pole will create an infinite electric field, before taking into account electric resistance breakdown of the air.)

To compute the electric field due to the bicycle frame, let's first say that the frame is 1m in height. Thus the two ends of the frame will have to carry voltages of +-600 volts with respect to the field produced by the overhead wires.

The actual electric field depends on how sharp the conductor is. Very sharp conductors have very large electric fields. Let's suppose that the bicycle seat has an effective radius of around 0.1 meters. What is the electric field at the seat?

Suppose that you have a point charge and that it produces a voltage of 600 volts at a radius of 0.1 meters, with 0 volts at infinity. What is the electric field at 0.1 meters? This is a question about the relationship between charge, potential and field. Some equations: $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r}$$ $$E = -\frac{1}{4\pi\epsilon_0}\frac{q}{r^2}$$ From these, we see that the electric field is increased by a factor of 1/r = 10/meter. Thus the field in the immediate vicinity of the bicycle seat is around $$ 600\;\; \textrm{volts} \times 10/\textrm{meter} = 6000 \;\;\textrm{volts / meter}.$$

It wouldn't surprise me that a sensitive part of the human anatomy could detect this electric field; it amounts to 60 volts per cm.

Most people have verified that if you touch your tongue to a 9 volt battery you can feel the shock. Now imagine a 50 volt battery jammed into your perspiring nether regions. This might very well feel like a lot of ants in your pants.

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My approach would be to treat yourself like the plate of a parallel-plate capacitor. Make the following assumptions:

eps = 9e-12

A = surface area of you + bike ~ 1 square meter

d = distance to power line ~20 meters

V = 1000 kV

Then the current is I = C*dV/dt = (eps*A/d)*(2*pi*50)*V = 140 microamps.

Now is it really possible to feel 140uA? According to the OSHA website, 1mA is the minimum current you can feel from your hand to your foot (http://www.osha.gov/SLTC/etools/construction/electrical_incidents/eleccurrent.html). So 140uA isn't that far off, and maybe you can make some argument about the current density being higher where it's funneled through the seat. More likely, your nerves are more sensitive in some areas of the body than others.

I highly doubt that at biking velocities there is any significant current from motion through the magnetic fields of the lines.

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what about treating the metal parts of the bike as an antenna and the body shorting it? –  anna v May 27 '12 at 9:23
    
Dear anna, something like what you say has to be right. Can one estimate it? What is the voltage that may be in the antenna? What is the electric field in the electromagnetic wave? When one multiplies it by one meter, one has to get the voltage that may be attached to the body. I am pretty sure that Brian's estimate is smaller by many, many orders of magnitude. –  Luboš Motl May 27 '12 at 17:09
    
Lubos, if you think 100uA is many, many orders of magnitude below what you're feeling under power lines, then please stay away from physics labs! A quarter amp could kill you under the right circumstances. As for the antenna model, look up the 'Hertzian' or 'short dipole' formula, which in the near field (under the power lines) reduces simply to the Laplace equation of electrostatics - i.e. you are a capacitor. See antenna-theory.com/antennas/shortdipole.php –  BrianC May 28 '12 at 2:49
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I am not sure that the following is relevant, but maybe what you feel is caused by the action of electric field on the hair on your skin. I wrote elsewhere on this web-site about this effect: "the electric field polarizes, rather than charges, hair, and then acts on the resulting electric dipoles, judging by the formulas in: "Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China, September 1-4, 2005", p. 4266. "Analysis of Body Hair Movement in ELF Electric Field Exposure", H. O. Shimizu, K. Shimizu. According to the formulas, it is essential that the electric field is not uniform. The authors claim good agreement with experimental results." It is also possible that, as others wrote here, metal parts of the bike modify the electric field, enhancing the effect.

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It's very interesting but from my basic school years, I became convinced that the effect of static electricity on hair is only relevant if the hair is dry etc. This sensation on the bike only occurs near the buttocks and groin area, I don't have so much hair to rely upon, and they're wet because I kind of sweat, anyway. So I don't believe the static electricity is really too relevant here. –  Luboš Motl May 27 '12 at 18:48
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I don't know. Maybe we are talking about different phenomena: you are talking about effects related to charging of hair, whereas there is no charging in the mechanism described in the quoted article. –  akhmeteli May 27 '12 at 18:56
    
Oh, I see, so this could also depend on my having body hair? ;-) –  Luboš Motl May 27 '12 at 19:20
    
Well, body hair is ubiquitous anyway :-) –  akhmeteli May 27 '12 at 19:43
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As Dmytry & BrianC said, you are spanning about 2m of a field gradient of about 5e4 v/m.

What's more, most of you and the bike are practically shorting out that 10%, since you are either metal or brine. So what voltage there is is dropping across fairly thin insulators - tires & clothing.

The current might be in the range of 1e-6 amps, and if that were going through the salt water of your body, you might not feel it. But if it hits your skin as a spark, you probably will feel it.

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Without calculating anything I can say that you are actually conducting electricity at 6ohz, the amperage is too small to harm because the resistance of your body combined with that also of the tires and the air overcomes the voltage. The salt in your perspiration does increase conductivity, the metal bike in a magnetic field does induce voltage much like a transformer does. I have felt the same effects when working near power lines of 345kv and handling any metal object. If you held a metal pole in the air high enough on a wet day near a power line it would kill you.

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