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Is the whole earth electric neutral? I know about the negative charge of the earths surface and the positive charge of the ionosphere, but i wonder if the whole earth (including its atmosphere) has an equivalent number of electrons and protons.

It could be measured by some space probe with devices to measure electric fields. Was this ever done?

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No, I won't say that.You answered it yourself the atmosphere is constantly being irradiated by ionizing radiation and some of the charged particles might leave the earth's atmosphere and hence would make the earth a charged object at least on a very small scale.

This question has been asked before, you can find a more detailed answer here.
The net charge of Earth

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