5. Vector Calculus

Stokes’ Theorem — Quiz

Test your understanding of stokes’ theorem with 5 practice questions.

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Practice Questions

Question 1

Which of the following best describes Stokes' Theorem?

Question 2

Which of the following is a necessary condition for applying Stokes' Theorem?

Question 3

Let $\mathbf{F}(x,y,z) = (-y, x, 2z)$. If $C$ is the circle $x^2 + y^2 = 1$, $z=0$, oriented counterclockwise, what is the value of the line integral $\oint_C \mathbf{F} \cdot d\mathbf{r}$?

Question 4

Which of the following vector fields has zero line integral around any closed curve in three-dimensional space, according to Stokes' Theorem?

Question 5

Suppose $\mathbf{F}(x,y,z) = (y, -x, z)$ and $C$ is the boundary of the surface $S$ given by $z = 1 - x^2 - y^2$ for $z \geq 0$. What is the value of $\oint_C \mathbf{F} \cdot d\mathbf{r}$?