12. Green’s Theorem

Flux Form — Quiz

Test your understanding of flux form with 5 practice questions.

Practice Questions

Question 1

What is the main statement of the flux form of Green's theorem for a vector field $\mathbf F=\langle P,Q\rangle$ on a region $R$ with boundary $C$?

Question 2

For $\mathbf F=\langle P,Q\rangle$, which boundary integral gives the outward flux across a positively oriented curve $C$?

Question 3

If $\nabla\cdot\mathbf F=0$ throughout a region $R$, what is the net outward flux across its positively oriented boundary $C$?

Question 4

What orientation does Green's theorem use for the boundary $C$ in its flux form?

Question 5

Find the outward flux of $\mathbf F=\langle x,y\rangle$ across the boundary of the rectangle $0\le x\le 2$, $0\le y\le 1$.