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This comment on r/AskPhysics says that the net charge of a closed universe must be $0$ because when you add all the electric field vectors, they cancel out completely. But shouldn't this be true of any electric charge? If a lone charged particle has its charge effectively neutralized, why should this not be the case when you have multiple charged particles? Isn't it like adding $0$ and $0$ to get a non-zero number?

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The comment you refer to is about net charge, it doesn't say anything about individual charges. That is you can have individual positively and negatively charged particles, but the sum over all the charges of all the particles in the universe must be zero.

The argument for the zero net charge goes as follows: Gauß's law states that the charge in a volume is proportional to the flux of the electric field through its surface, so for a closed universe you take the entire universe as volume and then the surface is an empty set, so the flux through it must be zero. From this we can conclude that the sum of all charges in the universe must be zero.

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  • $\begingroup$ I'm asking how it's any different when there are multiple charged particles. If the electric field from each particle by itself cancels out completely, why should it not cancel out when they're all put in the same space? Shouldn't they all combine linearly, meaning 0+0=0? $\endgroup$
    – zucculent
    Feb 16 at 2:04
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    $\begingroup$ Yes and my answer is, that that's based on a misunderstanding, the field of an individual particle does not cancel out. $\endgroup$ Feb 16 at 12:28

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