10. Vector Fields and Line Integrals

Work And Circulation — Quiz

Test your understanding of work and circulation with 5 practice questions.

Practice Questions

Question 1

What is the formula for the work done by a force field $\mathbf{F}$ on a particle moving along a curve $C$?

Question 2

Which expression represents the circulation of $\mathbf{F}$ around a closed curve $C$?

Question 3

If $\mathbf{F}$ is conservative, what is the work done by $\mathbf{F}$ around any closed curve?

Question 4

A constant force field $\mathbf{F}=\langle 3,4\rangle$ moves a particle along a straight line from $(0,0)$ to $(2,1)$. What is the work done?

Question 5

Let $f(x,y)=x^2+y^2$ be a potential function for $\mathbf{F}=\nabla f$. What is the work done by $\mathbf{F}$ from $(0,0)$ to $(1,1)$?