Gauss's law is more general than Coulomb's law, as it can be applied to both static and moving charges, regardless of their velocities or accelerations. While Coulomb's law is limited to stationary charges, the Lienard-Wiechert potentials are necessary for analyzing moving charges. Gauss's law remains valid since the divergence of the electric field (div E) equals 4π times the charge density (rho) in all scenarios. However, due to the loss of symmetry with moving charges, Gauss's law can only provide the integral of the electric field over a closed surface rather than the electric field at a specific point. The relationship between electric and magnetic fields, as described by Maxwell's equations, further illustrates why Gauss's law holds while Coulomb's law does not apply to moving charges.
