I’ve been searching for a proof, using the equation for the electric field due to a moving point charge – given, for example, on page 438 of the Third Edition of David Griffith’s Introduction to Electrodynamics (equation 10.65) – that Gauss’s law holds for a moving point charge. There is no such proof in Griffith’s textbook, or in the Third edition of Jackson’s Classical Electrodynamics, and the proof of Gauss’s law in the case of electrostatics that Jackson gives in the case of electrostatics on pages 27-8 would not seem to generalize to electrodynamics, since the varying retarded times and locations of the point charge giving rise to the electric field at different parts of the surrounding surface would seem to entail that one cannot add up the solid angles and arrive at the value 4π. The other textbook that I have is the Third Edition of Foundations of Electromagnetic Theory by John Reitz et al, and I have not been able to find any proof of Gauss’s law in the case of electrodynamics. (The last reference to Gauss’s law given in the index refers to page 336, and the Liénard-Wiechert equations for retarded potentials, followed by the general equations for the field due to a moving point charge, are not introduced until pages 470ff.) In short, does anyone know of a textbook where there is a proof, using the equations for the field due to a moving point charge, that Gauss’s law holds for a moving point charge? Thanks!