# Gauss' Law Conclusion in Gravitational Fields

• modulus
In summary, the conversation discussed the similarities between electric and gravitational fields, and how Gauss' Law applies to both. It also touched on the differences between electrostatic fields within a conductor and gravity.
modulus
I've been told that electric and gravitational fields have a lot in common, and both are practically analogous to each other. Also, the conclusions made through Gauss' Law apply just as well (analogously) to gravitational fields.

One of Gauss' Law's predictions is for a solid (conducting) charged body with a a cavity in it. According to it, no charge can exist inside the body...the only charge on it must exist on it's outer surface; that means no charge can exist on the inner surface. We get to that conclusion if we consider a Gaussian surface inside the body's material (not in the cavity).

But, if we introduce a point charge in the cavity, a charge develops on the inner surface, so that if we take a Gaussian surface in the body's material again (not in the cavity), there's no net electric field inside the body, and therefore, no net flux through the surface (and therefore, no net charge within the surface).

But, if we consider this for a gravitational field; we take a body with a cavity within it. For simplicity, I considered a spherical shell. I know that there's no gravitational field inside a shell. So, when I place a point mass inside the shell, why do we not observe any redistribution of the mass of the shell on the surface of the shell, so as to cancel out the gravitational field of the point mass (as we saw in the case of the point charge introduced in the cavity of the charged body). Or is there a tendency for a redistribution to take place...but it is not observable (or not possible, for that matter), because we consider the body to be rigid??

modulus said:
One of Gauss' Law's predictions is for a solid (conducting) charged body with a a cavity in it. According to it, no charge can exist inside the body...the only charge on it must exist on it's outer surface; that means no charge can exist on the inner surface. We get to that conclusion if we consider a Gaussian surface inside the body's material (not in the cavity).
That's only true because the electrostatic field within a conductor must be zero. That goes beyond Gauss' law and has no parallel with gravity. (Gauss' law itself works just fine for both.)

## 1. What is Gauss' Law Conclusion in Gravitational Fields?

Gauss' Law Conclusion in Gravitational Fields states that the net gravitational flux through any closed surface is directly proportional to the enclosed mass. In other words, the gravitational field created by a mass is directly proportional to the mass itself.

## 2. How is Gauss' Law Conclusion applied in gravitational fields?

Gauss' Law Conclusion is applied by using a Gaussian surface, which is a hypothetical surface that encloses the mass in question. The flux through this surface is then calculated using the gravitational field equation, and the mass enclosed is determined. This allows for the calculation of the gravitational field at any point in space.

## 3. What is the significance of Gauss' Law Conclusion in gravitational fields?

Gauss' Law Conclusion is significant because it provides a way to calculate the gravitational field at any point in space, without having to know the distribution of mass that created the field. This simplifies calculations and allows for a better understanding of the behavior of gravitational fields.

## 4. How does Gauss' Law Conclusion relate to Newton's Law of Universal Gravitation?

Gauss' Law Conclusion is a mathematical representation of Newton's Law of Universal Gravitation. It provides a more general and easier to use method for calculating gravitational fields, while Newton's law provides a more specific equation for calculating the force between two masses.

## 5. Can Gauss' Law Conclusion be applied to other types of fields?

Yes, Gauss' Law Conclusion can be applied to other types of fields, such as electric and magnetic fields. In these cases, the enclosed mass in the equation is replaced with the enclosed charge or current, respectively. This allows for the calculation of electric and magnetic fields using a similar method as in gravitational fields.

Replies
4
Views
2K
Replies
23
Views
1K
Replies
10
Views
1K
Replies
1
Views
271
Replies
8
Views
1K
Replies
5
Views
6K
Replies
12
Views
1K
Replies
4
Views
1K
Replies
28
Views
531
Replies
1
Views
1K