Static electricity: High voltage but low energy

Why so high voltage does not produce a danger current on human body?. I think that from a given value of voltage, current depends only on resistance. Why these machines produce always a low current. What is the mystery of static electricity?

First of all, it is not voltage that causes dangerous electric shock (e.g., ventricular fibrillation). It is a combination of the magnitude and duration of the current. And while the voltage delivered by the Van Der Graaf generator you describe may be very high, the current it delivers to the body lasts only an instant. (Very high energy generators, on the other hand, may be dangerous).

The Van Der Graaf generator is basically a charged capacitor. The energy stored in the electric field of a capacitor is given by

$$E=frac{1}{2}CV^2$$

So the capacitance required to store 2 J at 100,000 volts is 4 pF, or 4 x 10$^{-12}$F. Now consider the current that the generator can deliver to the body. According to IEC 60479-1, the internal body impedance is on the order of 500 $Omega$ hand to hand or hand to foot. The discharge current delivered to a resistor by a capacitor charged to voltage $V$ as a function of time is

$$i(t)=frac{V}{R}e^{frac{t}{RC}}$$

For 100,000 Volts and body resistance of 500 $Omega$ we have.

$$i(t)=200 e^{frac{t}{RC}}$$

In the equation, $RC$ is the time constant, or the time it takes for the current to be roughly 37 % of its initial value. In this case the time constant is 2 nanoseconds, or 2 x 10$^{-9}$s

So in 2 nanoseconds, the current falls to 74 amps. In 50 microseconds it falls to 4 x 10$^{-20}$A. In 1 microsecond its so small I get an error on my calculator.

The point is, these combinations of current and time, while may be sensed, are far below the thresholds of dangerous electric shock, per IEC 60479-1.

Hope this helps.