Gauss's law should be invalid if

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(B) Gauss's law is derived directly from Coulomb's law, which states that the electric force between two point charges is proportional to $1/r^2$. If

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The inverse square law were not exactly true

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(B) Gauss's law is derived directly from Coulomb's law, which states that the electric force between two point charges is proportional to $1/r^2$. If the inverse square law were not exactly true, the flux through a closed surface would not be directly proportional to the enclosed charge in the manner described by Gauss's law $(\Phi_E = q_{enclosed} / \epsilon_0)$. Therefore, the validity of Gauss's law is fundamentally dependent on the inverse square nature of the electric field.

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