How can I solve the following?
Let $F_1=(-y,x,z)$ and $F_2=(y,x,z)$. Calculate for each force field the work done in moving a particle around the circle in the $(x,y)$ plane. Which of the two force fields is conservative?
I know that the work done by a force $F$ on an object which undergoes an infinitesimal vector displacement $dr$ can be written as $dW = F \cdot dr$, where $dr = i\, dx+j\, dy+k\, dz$. Since the particle is moving around the circle in the $(x,y)$ plane then our integral should be from $0$ to $2\pi$ and we integrate with respect to $\theta$.