Gauss's Law applied to Gravational Flux

In summary, Gauss's Law states that the gravitational flux crossing a closed surface is -4piGM, where M is the mass inside the surface. When applied to a long straight cylinder with radius R and constant density p, the gravitational field at a distance r from the axis of the cylinder is proportional to r for r<R. The attempt at a solution shows that the factor of 2 is correct in the equation f = -2G(pi)pr, which is in agreement with others' results.
  • #1
dm9292
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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
 
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  • #2
I think the factor of 2 is correct.
 
  • #3
Thanks for confirming that
 

1. What is Gauss's Law applied to Gravational Flux?

Gauss's Law applied to Gravational Flux is a fundamental principle in physics that relates the distribution of matter within a closed surface to the gravitational field outside of that surface. It states that the net gravitational flux through a closed surface is equal to the enclosed mass multiplied by the gravitational constant.

2. How is Gauss's Law applied to Gravational Flux used in physics?

Gauss's Law applied to Gravational Flux is used in many different areas of physics, such as astrophysics, cosmology, and general relativity. It is a crucial tool for understanding the behavior of gravitational fields and can be applied to various systems, from planets and stars to entire galaxies.

3. What is the significance of Gauss's Law applied to Gravational Flux?

Gauss's Law applied to Gravational Flux is significant because it provides a mathematical framework for understanding the relationship between matter and gravity. It allows us to calculate the strength and direction of gravitational fields and make predictions about the behavior of celestial objects.

4. How is Gauss's Law applied to Gravational Flux related to Newton's Law of Gravitation?

Gauss's Law applied to Gravational Flux is a more general form of Newton's Law of Gravitation. While Newton's law only applies to point masses, Gauss's law can be applied to any distribution of mass. Additionally, Gauss's law is a fundamental principle in the development of Einstein's theory of general relativity.

5. Can Gauss's Law applied to Gravational Flux be violated?

No, Gauss's Law applied to Gravational Flux is a fundamental law of physics and has been well-tested and confirmed by numerous experiments and observations. Any violation of this law would require a fundamental shift in our understanding of the nature of gravity and the behavior of matter in the universe.

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