Divergence theorem requires a conservative vector field?

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SUMMARY

The divergence theorem does not require a conservative vector field to be applicable. The only requirement is that the vector function possesses continuous derivatives. This conclusion is supported by examples where nonconservative vector fields were successfully analyzed using the divergence theorem, demonstrating that the theorem's validity is independent of the field's conservativeness.

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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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