How much energy does a single lightning bolt from this Van De Graaff generator consume?

Question

I recently visited the Boston Museum of Science and saw a show using their "world's largest air-insulated Van de Graaff generator." I was curious as to the actual energy output of the generator. Apparently the generator operates at around 2 MV (source). I would love to know how much current flows at that voltage, to get a rough idea of how much energy each zap transfers.

I don't know a ton about physics and I'm sure I don't [yet] possess the skills to determine this on my own. Also, information and the exact specifications are surprisingly hard to find. It seems to be roughly 40 feet tall. That said, I wouldn't mind either a complete answer or a partial one that leaves some figuring for me to do - just wouldn't know where to start.

Answer 1

You can can get a rough estimate of the energy in the lightening bolt from this Boston van de Graaff high voltage generator by considering the electric energy stored in its dual sphere capacitor at its maximum voltage of V = 2MV. The charge of the capacitor is Q = C・V. The stored electric (electrostatic) energy of a capacitor is given by W = Q・V/2. A very rough estimate of the capacitance of the two cojoined capacitor spheres with radius r = 2.25m each would be C = 2・4π・𝛆 r, where 𝛆 is the absolute permittivity of air. This yields for C the capacitance estimate C = 501pF and for Q = 0.001002As. From this follows the stored electric energy W = 1002 J (Joule). With 1 cal = 4.18 J this gives 240 cal. Thus this energy would heat 240 ml water (one cup) by 1 degree Celsius. Assuming that this total estimated stored electric energy is released in a single "lightening bolt", this bolt energy would make a cup of coffee feel just a little bit warmer. Probably much less than one would expect considering the spectacular visual and acoustic effect!