Divergence theorem requires a conservative vector field?

AI Thread Summary
The divergence theorem does not require a conservative vector field; it can be applied to any vector field with continuous derivatives. A nonconservative vector field can still yield correct results when using the divergence theorem, as demonstrated in practice exams and homework problems. The key factor is the continuity of the derivatives of the vector function, not its conservativeness. Therefore, the divergence theorem is versatile and applicable beyond conservative fields. Understanding this distinction is crucial for correctly applying the theorem in various scenarios.
jesuslovesu
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Can anyone tell me whether or not the divergence theorem requires a conservative vector field? On a practice exam my professor gave a vector field that was nonconservative (I checked the curl) and proceeded to perform the divergence theorem to find the flux.

On one of my homework problems I forgot to check whether the field was conservative and it turns out that field was nonconservative but still got the correct answer. I don't know if that is a fluke or not.


In short: Do you need a conservative vector field in order to use the divergence theorem?
 
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jesuslovesu said:
In short: Do you need a conservative vector field in order to use the divergence theorem?

No. Only that the vector function have continuous derivatives.
 
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