Calculating Gravitational Potential Using Gauss's Law for a Thin Rod

In summary, we are trying to calculate the gravitational potential due to a thin rod using Gauss's law and integration. The person asking the question has attempted to solve it but did not get the same answer as with direct integration. They are seeking clarification on whether this method is valid and if not, why. They are also open to showing their work for potential mistake-spotting.
  • #1
tatiana_eggs
70
0

Homework Statement



Calculate the gravitational potential due to a thin rod of length l and mass M at a distance R from the center of the rod and in a direction perp. to the rod.

Homework Equations



integral form of Gauss's law wrt gravitation

The Attempt at a Solution



Can I use Gauss's law here i.e. solve for the gravitational field vector and integrate it to get gravitational potential? If not, why?

I tried but I don't get the same answer as with direct integration.
 
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  • #2
Yes, it should be possible to solve that way. You might want to try to show your work in case someone here can spot a mistake.
 

1. What is Gauss's Law and how does it relate to gravity?

Gauss's Law is a fundamental law in physics that explains the relationship between electric charges and electric fields. It states that the electric flux through a closed surface is proportional to the enclosed electric charge. This law also has an analogy in gravitation, known as Gauss's Law of Gravitation, which states that the gravitational flux through a closed surface is proportional to the enclosed mass.

2. How is Gauss's Law of Gravitation different from Newton's Law of Gravitation?

Newtons's Law of Gravitation is an inverse-square law that describes the force of gravity between two point masses. On the other hand, Gauss's Law of Gravitation is a law that describes the gravitational field itself, rather than just the force between masses. It allows us to calculate the gravitational field at any point in space, regardless of the distribution of mass.

3. Can Gauss's Law be applied to non-uniform distributions of mass?

Yes, Gauss's Law of Gravitation can be applied to both uniform and non-uniform distributions of mass. However, in order to use the law for non-uniform distributions, we need to divide the distribution into small, infinitesimal pieces and calculate the gravitational field at each individual point. Then, we can integrate these values to find the total gravitational field at a specific point.

4. How does the shape of an object affect the gravitational field according to Gauss's Law?

The shape of an object does not affect the gravitational field according to Gauss's Law. The law states that the gravitational flux through a closed surface is proportional to the enclosed mass, regardless of the shape of the surface. This means that the gravitational field at a point outside of a spherical object will be the same as the field outside of a cube with the same mass.

5. How does Gauss's Law of Gravitation relate to the concept of escape velocity?

Gauss's Law of Gravitation can be used to calculate the escape velocity of an object from the surface of a planet or other massive object. By setting the gravitational potential energy of the object equal to its kinetic energy at the point of escape, we can solve for the escape velocity. This is a direct application of Gauss's Law of Gravitation in determining the dynamics of objects in a gravitational field.

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