In electrostatics we say that Gauss' law and
Coulomb's law are equivalent. But Gauss' law
is one of Maxwell's equations. It means the
law is also valid when charges are in motion.
I am thinking about a single point charge
moving inside a spherical gaussian surface
(at rest with respect to an inertial frame).
1) Can one say that Gauss' law is always valid?
2) Should one say that the law is valid (to a good
approximation) only at non-relativistic velocities?
My guess is that only #2 is correct.
Ludwik Kowalski