Re: Gauss law again

[Ludwik Kowalski <kowalskil@MAIL.MONTCLAIR.EDU>]

On Sunday, Dec 21, 2003 Ludwik Kowalski wrote:

> 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

Why am I asking this question?
Suppose a particle moves along a horizontal
diameter from left to right. The density of E
lines at the left side of the sphere is decreasing
while the density at the right side is increasing.
But due to the finite speed of propagation of
disturbances the rates at which the density is
changing (at any given moment) can not be
the same on both sides.

Suppose v=0.99*c. Suppose the particle is
already very close (x=0.9*R) to the right side
of the sphere. A small additional displacement
already resulted in a change of density at the
right side. But the left side "was not yet
informed" that the displacement occurred.
How can the total flux of E lines remain
constant is such situations.
Ludwik Kowalski