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From a pre-academic studies book, the example uses a gaussian surface outside of the charged sheet to show that because the flux through it is 0, the field on both ends has to be equal. Is this a valid use of Gauss's law?

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Yes, it is. The Gauss law $$\int_S \vec E.d\vec S={Q_{\rm int}\over\varepsilon_0}$$ applies to all closed surface $S$.

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