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I was doing homework, and the following appeared as a question:

A negatively charged thundercloud above Earth's surface may be modeled by a parallel plate capacitor. The lower plate of the capacitor is the Earth's surface and the upper plate is the base of the thundercloud.

After being asked to find things like capacitance and total energy, the last question is,

State one assumption that needs to be made so that the Earth-Thundercloud system may be modeled by a parallel plate capacitor

The answer I wrote was, "There is no energy lost as heat during the discharge"

My instructor marked this as incorrect. Isn't some energy lost in the creation of plasma, or during the friction at which the lightning is created?

Thank you for your help.

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  • $\begingroup$ There is indeed energy lost as heat during the discharge, but commercial parallel plate capacitors also lose energy as heat (some can even explode due to the heat if you are not careful), so I would not say it is a necessary assumption. On the other hand one of the requirements for a system to be called a "capacitor" is for it to be electrically neutral (if one plate has charge $q$, the other one has to have charge $-q$). $\endgroup$ – S V Sep 27 at 16:42
  • $\begingroup$ Notice that capacitors do not discharge via a spark from plate to plate. Also, the model is not for the actual lightning flash, but for the build-up of charge prior to the flash. So you are mixing events, it seems to me, and the question is not about the discharge. That's why your answer is incorrect. $\endgroup$ – Bill N Sep 27 at 17:34
  • $\begingroup$ A good argument can be made that all of the energy is lost as heat. $\endgroup$ – David White Sep 27 at 20:20
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The capacitor analogy of the lightning event is that the dielectric material between the capacitor plates undergoes dielectric breakdown because the voltage is too high. Dielectric breakdown of an insulating material involves high discharge currents that, in turn, generates heat. For organic solid insulation, the breakdown is destructive and permanent causing carbonization of the material. It permanently loses its insulating properties.

For the lightning event it is the avalanche current associated with the dielectric breakdown of the air, again due to the voltage exceeding the dielectric strength of the air, that generates heat. But air is a renewable insulation. So once the high voltage is gone, its excellent insulating properties return.

Hope this helps.

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There is indeed energy dissipation as heat during a lightning event. However, the lightning event would only occur in the first place when the Earth-Thundercloud system is no longer acting as a parallel plate capacitor. You answered with a fact that does not address the premise.

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