Re: Gauss law again

[John Denker <jsd@AV8N.COM>]

Quoting Ludwik Kowalski <kowalskil@MAIL.MONTCLAIR.EDU>:

> In electrostatics we say that Gauss' law and
> Coulomb's law are equivalent.

Yes, and more generally than that, they are equivalent.

> But Gauss' law is one of Maxwell's equations.

And/or you could say Coulomb's law is one of the
Maxwell equations.

> 1) Can one say that Gauss' law is always valid?

Yes.

> 2) Should one say that the law is valid (to a good
> approximation) only at non-relativistic velocities?

  Tangential remark: The Maxwell equations are 100% relativistically
  correct.  There is no halfway point between statics (zero velocity)
  and full-blown electrodynamics (all velocities, including
  relativistic).

But to address the original question:  The Coulomb (or Gauss)
law is *one* of the Maxwell equations.  It is always true, but
it is not always a complete description of the electric field.
The other contribution comes from changing magnetic fields ...
and is divergence free, so it cannot conflict with the
Gauss/Coulomb equation.