A position-dependent force field in the horizontal $xy$-plane is given by $\vec{F} = b y\,\hat{i}$, where $b$ is a positive constant. A particle is carried along a closed square path in the $xy$-plane with vertices at $(0,0)$, $(L,0)$, $(L,L)$, and $(0,L)$, traversed in the counterclockwise direction. What is the net work done by the force on the particle during one complete circuit around the loop?