The statement from which I want to start is this (taken from the Feynman Lecture):
On an ordinary day over flat desert country, or over the sea, as one goes upward from the surface of the ground the electric potential increases by about 100 volts per meter.
It is easily described by this picture.
My first question is:
1) why we are not crossed by a current in our body? Consider a person with 1.8m height: he should be crossed by, if for instance we consider a mean value of human body resistance equal to 10kOhm, 180V/10kOhm = 18mA of current, that is quite high for human body. We will surely perceive it, since it is similar to that we perceive if we touch the phase of our home electric network.
A first answer comes from the Feynmann Lecture, which states that, since the human body is a conductor, we have this situation:
So, If I have understood it correctly, no current flows because no voltage is applied between head and feet of our body. There is a voltage between air and our head, but air is a good dielectric and so no current will flow. But there are many things I do not understand:
1.1) The Human Body is not a perfect electric conductor, therefore its surface will be equipotential only after a certain transient in which all the charges have been distributed on all the body. During this transient, we shoud have perceived the current across our body.
1.2) Apart from the question about the transient, I do not understand this general explanation. In fact, a conductor keeps equipotential at equilibrium, as we have just said. But this situation is different. I see it in this way:
From this scheme, we conclude that the body should be crossed by 18mA of current.
1.3) Suppose our shoes are able to isolate the body from the earth. How does the situation change? I'd say that, from a circuital point of view, it is like in 1.2 (a floating node connected to the earth will not affect the current of the circuit):
Also in this case, the body should be crossed by 18 mA of current.
Now let's go to my second question.
Let's consider a certain component, for instance a LED, and let's put it with its anode towards sky. the physical distance between its terminals (enlarged and elongated with copper wires, for instance) may be, for instance, 5cm.
So the voltage on it shoud be equal to:
100V/m * 0.05m = 5V
2) Why does it keep off and is not switched on?