Re: [Phys-l] Gauss' Law

["Alfredo Louro" <louro.alfredo@gmail.com>]

On Tue, Mar 4, 2008 at 11:09 AM, Robert Carlson
<rcarlson@physicstoolkit.com> wrote:

>  Now, my understanding of Gauss' Law is that it only
>  tells me what the gravitational field is on the
>  Gaussian surface due to the mass inside the Gaussian
>  surface.  It does not tell me anything about the
>  gravitational field on the Gaussian surface due to
>  mass outside the surface.

Actually, Gauss' theorem does tell you something about the sources
outside the Gaussian surface, and if the field is nice and
symmetrical, it tells you everything you need to know.

Gauss' theorem implies that the flux through a closed surface due to
sources outside it, is zero. If the field has, for example, spherical
symmetry and you choose a sphere as a Gaussian surface, then the field
over the surface is uniform, and perpendicular to the surface. Then
the only way you can get zero flux is if the field is uniformly zero
over the surface.

By integrating, numerically or analytically, of course you will get
the same result, but this does not give more information than Gauss'
theorem. G's theorem is just a very elegant way of doing the
integration for you.

Alfredo