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A law in classical electromagnetism and Newtonian gravity which relates (charge) density to the divergence of a field, or alternatively the charge in a volume to the flux through the bounding surface.
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Electric flux density for a hollow cylinder using Gauss's law
The highlighted part is implying that the total charge on the inner surface of the outer cylinder is equal and opposite to the total charge on the outer surface of the inner cylinder.
First, note th …