Gauss’ Law says that the only thing that matters to calculating our flux integral ∮E•dA is the charge within the closed mathematical surface. Or, conversely and necessarily, any E-field manifested by any external charges (or arbitrary arrangement thereof) would result in a positive and negative contribution to the flux integral that exactly cancels out…no matter how bizarre the external field and no matter how bizarre the mathematical surface.Prove

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Gauss’ Law says that the only thing that matters to calculating our flux integral ∮E•dA is the charge within the closed mathematical surface. Or, conversely and necessarily, any E-field manifested by any external charges (or arbitrary arrangement thereof) would result in a positive and negative contribution to the flux integral that exactly cancels out…no matter how bizarre the external field and no matter how bizarre the mathematical surface.

Prove this to me. Provide a logical argument in bullet point form using sound physical reasoning…with a few equations and diagrams if needs be. SEE PICTURE ATTATCHED!!

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