5. Vector Calculus

Conservative Vector Fields And Potential Functions — Quiz

Test your understanding of conservative vector fields and potential functions with 5 practice questions.

Practice Questions

Question 1

Which of the following conditions is necessary for a vector field $\mathbf{F}(x,y)$ to be conservative in a simply connected region?

Question 2

If $\mathbf{F}(x,y) = (2x, 3y)$, what is a potential function $f(x,y)$ for this vector field?

Question 3

Which of the following vector fields is NOT conservative?

Question 4

What is the curl of the vector field $\mathbf{F}(x,y,z) = (2y, 3z, 4x)$?

Question 5

If $\mathbf{F}(x,y,z) = (x, y, z)$, what is a potential function $f(x,y,z)$ for this vector field?