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Starting here:

http://hypertextbook.com/facts/1998/TreshaEdwards.shtml

"Over land the average electric field is about 120 V/m …. Assuming an exponential increase of the conductivity with altitude, it can be shown that the electric field decreases exponentially with altitude. At the 30-km level, the electric field is as low as 300 MV/m [sic]. Integrating the electric field from the earth's surface to the ionosphere gives as a result an electric potential difference of about 200 kV." Standardized result: 0.300–120 V/m

Since this is the case, how come a conductor placed in this field doesn't immediately have a powerful current running through it?

This is my primitive understanding of the situation:

schematic

simulate this circuit – Schematic created using CircuitLab

But clearly this must be wrong, because you don't get 120 Amps through any random string of wire that happens to hang vertically so what am I missing?

EDIT

Is this a more reasonable approximation?

schematic

simulate this circuit

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The reason you don't get a powerful current is that the conductivity of air is so low. Since the conductivity of the copper wire is so much higher, the electric field itself is modified.

Basically, charges do move around in the copper wire, which means that you have to consider the entire wire to be at the same potential. This causes the nominally vertical field lines of the Earth to be warped in the vicinity of the wire — or any other conductive object, such as a human body. In a short period of time, the charge distribution and the modified field reach a new equilibrium state.

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    \$\begingroup\$ And one could still measure it if he have a high input impedance voltmeter , Am I right ?If I could find a voltmeter which gives me the internal resistance of air then I could measure it. Am I right ? \$\endgroup\$ Jun 25 '14 at 13:17
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    \$\begingroup\$ Yes, such voltmeters exist, and are also useful in ESD work for measuring the surface charge on objects. \$\endgroup\$
    – Dave Tweed
    Jun 25 '14 at 14:31

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