1.
A standard example is the outward Flux of \(\vec{F}=x\hat{i}+y\hat{j}+z\hat{k}\) across unit sphere of radius a centered at the origin. Compute this with the Divergence theorem.
Answer.\(4\pi a^3\)
Section 8.2 Divergence Theorem Example
This video uses a cube as an example, which is great because doing six surface integrals (for the six sides) would be annoying but the divergence theorem makes it easy.
Learning Objectives:
- Compute Flux using the Divergence Theorem
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2.
Ok, I said this one was easier to use the Divergence Theorem. But it is actually a reasonable exercise on computing the surface integrals directly. Yes there are six for the six sides but at least three are zero and you can use symmetry for the others. So verify you get the same answer directly as using Divergence Theorem.
