Cyclist's electrical tingling under power lines 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.

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

 A: 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.
A: 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.
A: 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 $1 pT$.  

(**) 1 Sep 2014 update.  Dmytry very astutely points out in a comment that there will be local electric field intensification effects from conductive irregularities in the otherwise flat ground surface, such as our cyclist (who, being somewhat sweaty, will have a conductive surface).  The same principle applies to lightning rods.
For the proverbial spherical cyclist, the local field will be increased by a factor of 3, independent of the sphere's size, as long as it's much less than the distance to the power line.  It turns out that it doesn't matter whether the sphere is grounded or insulated, since its total charge remains 0.  
For more elongated shapes the intensification can be much higher:  for a grounded prolate spheroid with 10:1 dimensions, the multiplication factor is 50.  This intensification of course enhances any sensation one might feel. 
A: 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. 
A: 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.
A: 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.
A: 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.
