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title: "A two-dimensional electrostatic potential in the first quadrant of the \\(xy\\)-plane is represented by four equipotential contours labeled \\(40\\text{ V}\\), \\(30\\text{ V}\\), \\(20\\text{ V}\\), and \\(10\\text{ V}\\). Along the positive \\(x\\)-axis, the contours are perpendicular to the \\(x\\)-axis with a uniform spacing of \\(1.0\\text{ cm}\\), decreasing in potential in the \\(+x\\)-direction, and point \\(P\\) lies on the \\(20\\text{ V}\\) contour on this axis. Along the positive \\(y\\)-axis, the contours are perpendicular to the \\(y\\)-axis with a uniform spacing of \\(2.0\\text{ cm}\\), decreasing in potential in the \\(+y\\)-direction, and point \\(Q\\) lies on the \\(20\\text{ V}\\) contour on this axis. Which of the following diagrams best represents the direction and relative magnitude of the electric field vectors, \\(\\vec{E}_P\\) and \\(\\vec{E}_Q\\), at points \\(P\\) and \\(Q\\)?"
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url: "https://nerd-notes.com/ubq/124738/"
date_modified: "2026-09-28T14:09:33+00:00"
---

# A two-dimensional electrostatic potential in the first quadrant of the \(xy\)-plane is represented by four equipotential contours labeled \(40\text{ V}\), \(30\text{ V}\), \(20\text{ V}\), and \(10\text{ V}\). Along the positive \(x\)-axis, the contours are perpendicular to the \(x\)-axis with a uniform spacing of \(1.0\text{ cm}\), decreasing in potential in the \(+x\)-direction, and point \(P\) lies on the \(20\text{ V}\) contour on this axis. Along the positive \(y\)-axis, the contours are perpendicular to the \(y\)-axis with a uniform spacing of \(2.0\text{ cm}\), decreasing in potential in the \(+y\)-direction, and point \(Q\) lies on the \(20\text{ V}\) contour on this axis. Which of the following diagrams best represents the direction and relative magnitude of the electric field vectors, \(\vec{E}_P\) and \(\vec{E}_Q\), at points \(P\) and \(Q\)?

A two-dimensional electrostatic potential in the first quadrant of the \(xy\)-plane is represented by four equipotential contours labeled \(40\text{ V}\), \(30\text{ V}\), \(20\text{ V}\), and \(10\text{ V}\). Along the positive \(x\)-axis, the contours are perpendicular to the \(x\)-axis with a uniform spacing of \(1.0\text{ cm}\), decreasing in potential in the \(+x\)-direction, and point \(P\) lies on the \(20\text{ V}\) contour on this axis. Along the positive \(y\)-axis, the contours are perpendicular to the \(y\)-axis with a uniform spacing of \(2.0\text{ cm}\), decreasing in potential in the \(+y\)-direction, and point \(Q\) lies on the \(20\text{ V}\) contour on this axis. Which of the following diagrams best represents the direction and relative magnitude of the electric field vectors, \(\vec{E}_P\) and \(\vec{E}_Q\), at points \(P\) and \(Q\)?

![A two-dimensional Cartesian coordinate frame showing the first quadrant with a horizontal axis labeled x and a vertical axis labeled y meeting at an origin labeled O. Four nested quarter-elliptical dashed curves extend from the positive y-axis to the positive x-axis. Along the horizontal axis, the four dashed curves intersect perpendicularly with uniform spacing of 1.0\text{ cm} and are labeled 40\text{ V}, 30\text{ V}, 20\text{ V}, and 10\text{ V} from left to right. A solid dot on the horizontal axis at the 20\text{ V} curve is labeled P. Along the vertical axis, the four dashed curves intersect perpendicularly with uniform spacing of 2.0\text{ cm} and are labeled 40\text{ V}, 30\text{ V}, 20\text{ V}, and 10\text{ V} from bottom to top. A solid dot on the vertical axis at the 20\text{ V} curve is labeled Q. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-diagram-1-1790604571-TH5mTX.jpg)

- **A.** Diagram A
- **B.** Diagram B
- **C.** Diagram C
- **D.** Diagram D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124738/*