Divergence Theorem $$\oint_S \vec F\cdot\hat n\,dS=\int_V \nabla \cdot \vec F\,dV$$

We want to prove $$\oint_S T\cdot\hat n\,dS=\int_V \nabla T\,dV.$$

In the proof we take $\vec F= T\hat c$ and we got $ \nabla \cdot \vec F=\hat c\cdot\nabla T$

Question: How can we be sure that $\vec F= T\hat c$ is always true ? What is the mathematical reasoning?

  • 1
    $\begingroup$ What does the proof say that $\hat{c}$ is? Doesn't it say something like "Let $\hat{c}$ be a constant vector field and set $\vec{F} = T \hat{c}$? $\endgroup$ – md2perpe Nov 8 '18 at 20:55

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.