Physical Examples of Divergence Theorem

In summary, the conversation discusses the use of divergence theorem in finding real life applications and showing the equivalence between integral and differential forms of conservation laws. The person has already used it to demonstrate Gauss' law for electric charge, but is looking for another example for gravity. They mention that fluid mechanics may heavily utilize these integral theorems.
  • #1
Diracster
3
0

Homework Statement


This problem I have been set is to find real life applications of divergence theorem. I have to show the equivalence between the integral and differential forms of conservation laws using it.

2. The attempt at a solution

I have used div theorem to show the equivalence between Gauss' law for electric charge enclosed by a surface S. But can't think or find of another example other than that for Gravity. The problem is that I need to find a different example to Gravity as that is the next question and I can't imagine they would ask the same question twice!
Any suggestions of fields of physics that I can look into would be really helpful. Thanks in advance.




Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
  • #2
iirc, Fluid Mechanics heavily uses these integral theorems from Vector Analysis.
 

1. What is the divergence theorem?

The divergence theorem, also known as Gauss's theorem, is a mathematical concept in vector calculus that relates the flow of a vector field through a closed surface to the divergence of the vector field within the volume enclosed by the surface.

2. How is the divergence theorem applied in physics?

The divergence theorem is commonly used in physics to calculate the flux of a vector field, which is the amount of fluid or energy flowing through a surface. It is also used to relate the volume integral of a vector field to the surface integral of its normal component.

3. Can you give an example of the divergence theorem in action?

One example of the divergence theorem in action is calculating the flow of air through a closed surface, such as a balloon. The divergence of the velocity field of the air within the balloon is related to the net flux of air through the surface of the balloon.

4. What is the difference between the divergence theorem and the divergence of a vector field?

The divergence theorem is a mathematical relationship that relates the surface integral of a vector field to the volume integral of its divergence. The divergence of a vector field, on the other hand, is a mathematical operation that calculates the amount of "outwardness" of a vector field at a particular point.

5. How is the divergence theorem related to other theorems in vector calculus?

The divergence theorem is closely related to other important theorems in vector calculus, such as Stokes' theorem and Green's theorem. These theorems all involve integrating vector fields over surfaces and volumes and are fundamental concepts in the study of electromagnetism and fluid dynamics.

Similar threads

  • Introductory Physics Homework Help
Replies
12
Views
4K
  • Calculus and Beyond Homework Help
Replies
28
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
Replies
11
Views
5K
  • Introductory Physics Homework Help
Replies
25
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
119
  • Introductory Physics Homework Help
Replies
3
Views
442
  • Special and General Relativity
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
3K
Back
Top