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So essentially I want to make a 1,000,000 volt Van de Graaff machine and I'm trying to calculate the energy that would pass through the human body if I charged it completely and let it arc to my hand. I may be doing many things wrong here but theoretically with a voltage of 1,000,000 volts we can calculate the current through my body by dividing by the human body's resistance. Being about 500 ohms the current should be about 2,000 amps. The power is then 2,000,000 watts. Then to find the energy I believe I have to use the equation joules = watts * seconds but I'm not sure where to find a measurement on how long it will take to pass through my body. This is where I'm stuck: any help is appreciated.

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    $\begingroup$ You’re current calculation assumes the generator is an ideal voltage source. In reality it’s only capable of delivering current on the order of microamperes, way below levels harmful to humans $\endgroup$
    – Bob D
    Commented Jan 19, 2020 at 22:44
  • $\begingroup$ If thats true how can i calculate the current? $\endgroup$ Commented Jan 19, 2020 at 22:45
  • $\begingroup$ It is difficult to estimate the specifications of electrostatic machines in advance. One can measure the current with a multimeter. Or by looking at the brightness of a LED. Current increases with the speed of the belt. (I doubt you will be able to build a 1 MV generator.) $\endgroup$
    – user137289
    Commented Jan 20, 2020 at 0:33
  • $\begingroup$ Where did that figure of 500 ohms come from? That seems way too low to me, unless a very high voltage is already passing through the body (and hence causing electrochemical changes). See en.wikipedia.org/wiki/Electrical_injury#Body_resistance $\endgroup$
    – PM 2Ring
    Commented Jan 20, 2020 at 6:33

3 Answers 3

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It is typically difficult to determine the duration of the discharge in this kind of situation.

It would be easier to work out how much energy is initially stored on the generator. This sets an upper limit on how much energy could be delivered to your body when you contact it.

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  • $\begingroup$ How might i go about this because as far as i know to calculate energy you must know the time? $\endgroup$ Commented Jan 19, 2020 at 22:47
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    $\begingroup$ The VdG generator electrode is part of a capacitor. You need to know the charge on it and its capacitance (which depends on how it's situated relative to the ground). Then you can use the well-known formula for the energy stored in a capacitor as function of its voltage. $\endgroup$
    – The Photon
    Commented Jan 19, 2020 at 22:49
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I would rather compare it with the speed of the neural activity. A signal in your body would move by around 10 m/s if not some tricky feature allowing it to jump, increasing its speed tenfold. Typically a signal travels on a 100 m/s speed, except a few of them like pain, which is slower.

Since those are also electric signals (just fueled by Kalium/Natrium pumps in your body) and the cable equation also works on them, i would say an external current's speed should be comparable!

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For safety it is advisable not to use capacitors that store more than 1 milli-joule. So no large Leyden jars in schools. A suitable size were those film canisters in the era of analog photography.

The energy stored in a capacitor is $E = CV^2/2.$ So at $10$ kV the capacitance should not be larger than about $2.10^{-11}$ F = $20$ pF.

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