---
title: "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?"
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url: "https://nerd-notes.com/ubq/117611/"
date_modified: "2026-08-04T07:49:19+00:00"
---

# 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?

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?

![A two-dimensional Cartesian coordinate system with a horizontal axis labeled x and a vertical axis labeled y. A square path of side length L in the first quadrant has vertices at (0,0), (L,0), (L,L), and (0,L). Arrowheads along the four sides of the square indicate a counterclockwise traversal: rightward along the bottom edge from (0,0) to (L,0), upward along the right edge from (L,0) to (L,L), leftward along the top edge from (L,L) to (0,L), and downward along the left edge from (0,L) to (0,0). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829759-LYAx0t.jpg)

- **A.** \(0\)
- **B.** \(-b L^2\)
- **C.** \(b L^2\)
- **D.** \(\dfrac{1}{2} b L^2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117611/*