Physical Examples of Divergence Theorem

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SUMMARY

The discussion focuses on real-life applications of the Divergence Theorem, specifically in demonstrating the equivalence between integral and differential forms of conservation laws. The user successfully applied the theorem to Gauss' law for electric charge but seeks additional examples beyond gravitational fields. Fluid mechanics is highlighted as a significant area where the Divergence Theorem is utilized, indicating its relevance in various physical contexts.

PREREQUISITES
  • Understanding of the Divergence Theorem in vector calculus
  • Familiarity with Gauss' law in electromagnetism
  • Basic concepts of fluid mechanics
  • Knowledge of conservation laws in physics
NEXT STEPS
  • Research applications of the Divergence Theorem in fluid dynamics
  • Explore the role of the Divergence Theorem in electromagnetism beyond Gauss' law
  • Investigate the use of the Divergence Theorem in thermodynamics
  • Study examples of the Divergence Theorem in environmental physics, such as pollutant dispersion
USEFUL FOR

Students and professionals in physics, particularly those studying vector calculus, electromagnetism, and fluid mechanics, will benefit from this discussion.

Diracster
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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

 
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iirc, Fluid Mechanics heavily uses these integral theorems from Vector Analysis.
 

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