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Re: [Phys-l] Gauss' Law



|It's not clear to me, using symmetrical
| arguments, how one can establish that the mass outside the
| Gaussian surface in these situations contributes zero
| gravitational field on the Gaussian surface.

The symmetry argument, or the fact that a spherical distribution of
matter outside the Gaussian Surface (centered on the center of the
spherical distribution) is crucial to the argument; so if you do not
follow that you are missing something.

|
| One can of course start with a spherical or infinite
| cylindrical shell of mass and integrate using Newton's Law of
| Gravitation as is done in Tipler for a spherical shell. Then
| having the knowledge that the field is zero inside these
| shell distributions, one can conclude that the mass outside
| the Gaussian surface for uniform volume mass densities for
| spherical or cylindrical distributions contributes nothing on
| the Gaussian surface and only the mass inside is important.

That works.

|
| So, it appears to me, that one must first show that the
| gravitational field is zero inside a spherical shell or
| infinitely long cylindrical shell of mass without using
| Gauss' Law, before we can use Gauss' Law to find the field
| inside uniform volume mass density spherical or infinitely
| long cylindrical mass configurations.

More or less correct. Using Gauss's Law to determine the field requires
more than Gauss's law, for the simple reason that knowing the result of
an integral does not uniquely determine the integrand. So you can not
do it from Gauss's law alone. The something else you need is the extra
information obtained from symmetry arguements. In the example above,
the spherical shell's field inside the shell can be deduced either from
direct integration or from symmetry arguements combined with Gauss's
law.