Is Gauss's Law Valid for Moving Charges?

[assed]

I found in this forum an old thread regarding this topic, but as it didn't have (in my opinion) a satisfactory answer, I decided to open a new one.
Usually when one begins to study Electromagnetism, Coulomb's law in introduced as an experimental result valid for static point charges. From Coulomb's law, some books then derive Gauss's law. What has ben bothering me is that when it comes to electrodynamics, therefore with moving charges, the books (at least the ones I've read) only briefly mention that Gauss's law is still valid. I ask if someone here knows if this is a result primarily obtained from experiment ( and if so, when and who did it?) or it can be seen with a theoretical argument.
By the way, before someone suggests to apply the divergence to a calculated electric field of moving charges, I don't think it is reasonable, once these field are obtained as solutions to Maxwell's equations which include Gauss's law.
Thanks

 

[vanhees71]

Of course, the validity of Maxwell's equations as a description of real phenomena cannot be mathematically proven. They provide a theory of such a description that is subject to empirical testing, i.e., you make predictions for observations from them and compare to (experimental) observations in nature. So far, we have no evidence that the Maxwell equations fail (within the boundaries of applicability of the classical-field-theory approximation to quantum electrodynamics). That's why we think that they are a valid description of electromagnetical phenomena.

 

[Meir Achuz]

Maxwell's equations, including div E=4 pi rho, are relativistically covariant.
Gauss's law is experimentally verified for a charge at rest.
If you accept Special Relativity, Gauss's law holds for a charge in motion.