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 is a necessary condition for a vector field $\mathbf{F}(x,y) = (M(x,y), N(x,y))$ to be conservative in a simply connected region?

Question 2

If $\mathbf{F}(x,y) = (2x, 3y^2)$, what is the potential function $f(x,y)$ such that $\nabla f = \mathbf{F}$?

Question 3

Which of the following vector fields is conservative?

Question 4

What is the potential function $f(x,y)$ for the conservative vector field $\mathbf{F}(x,y) = (3x^2 - 4y, -4x + 6y^2)$?

Question 5

Which statement is true about a vector field $\mathbf{F}(x,y)$ that has a potential function $f(x,y)$?