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Gauss's Law applied to Gravational Flux

  • Thread starter dm9292
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  • #1
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Homework Statement


Gauss's Law states that the gravatational flux crossing a closed surface is -4piGM, where M is the mass inside the surface.

A Long straight cylinder has a radius R and is made of material of a constant density of p
Show that the gravatational field at a distance r from the axis of the cylinder is proportional to r, for r<R.

Homework Equations



f.da = (closed integral) -4piGM

The Attempt at a Solution



I enclosed the cylinder in a Gaussian surface

Mass Enclosed is pi(r)^2lp
f is constant therefore, f.da = f.2(pi)rl

So by gauss's law:

f.2(pi)rl = -4piG[pi(r)^2lp]

So f = -2G(pi)pr.

The problem is when i compare with people they get f = -G(pi)pr.

Is this correct? Either shows that f proportional to r. But the constant 2 is confusing me, should it be there or not?

Any help would be greatly appreciated
 

Answers and Replies

  • #2
Dick
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I think the factor of 2 is correct.
 
  • #3
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Thanks for confirming that
 

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