Gauss's law can be derived from Coulomb's law, but not vice versa, suggesting they are not logically equivalent. The Coulomb field is divergenceless except at the charge's location, allowing for consistent flux calculations through any surface containing the charge. Evaluating the flux using a spherical surface leads to Gauss's law for point charges, which can be extended to any charge distribution through superposition. Most introductory electromagnetism textbooks present Coulomb's law first and then derive Gauss's law from it. This indicates that while they are closely related, their derivation order highlights their distinct foundational roles in electromagnetism.
