---
title: "The electric potential \\(V\\) as a function of position \\(x\\) along the \\(x\\)-axis in an isolated region is shown in the graph. The profile consists of a parabolic curve with its vertex at \\((1\\text{ m}, 4\\text{ V})\\) extending from \\(x = 0\\) to \\(x = 2\\text{ m}\\), a linear segment from \\(x = 2\\text{ m}\\) to \\(x = 4\\text{ m}\\), and a horizontal line from \\(x = 4\\text{ m}\\) to \\(x = 6\\text{ m}\\). Which of the following statements correctly describes the electric field component \\(E_x\\) in this region?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/124555/"
date_modified: "2026-09-28T14:08:37+00:00"
---

# The electric potential \(V\) as a function of position \(x\) along the \(x\)-axis in an isolated region is shown in the graph. The profile consists of a parabolic curve with its vertex at \((1\text{ m}, 4\text{ V})\) extending from \(x = 0\) to \(x = 2\text{ m}\), a linear segment from \(x = 2\text{ m}\) to \(x = 4\text{ m}\), and a horizontal line from \(x = 4\text{ m}\) to \(x = 6\text{ m}\). Which of the following statements correctly describes the electric field component \(E_x\) in this region?

The electric potential \(V\) as a function of position \(x\) along the \(x\)-axis in an isolated region is shown in the graph. The profile consists of a parabolic curve with its vertex at \((1\text{ m}, 4\text{ V})\) extending from \(x = 0\) to \(x = 2\text{ m}\), a linear segment from \(x = 2\text{ m}\) to \(x = 4\text{ m}\), and a horizontal line from \(x = 4\text{ m}\) to \(x = 6\text{ m}\). Which of the following statements correctly describes the electric field component \(E_x\) in this region?

![A Cartesian coordinate plot showing a single solid curve representing electric potential \(V\) as a function of position \(x\). The horizontal axis is labeled \(x\text{ (m)}\) with tick marks and integer labels at 0, 1, 2, 3, 4, 5, and 6. The vertical axis is labeled \(V\text{ (V)}\) with tick marks and labels at -6, -4, -2, 0, 2, 4, and 6. From \(x = 0\) to \(x = 2\text{ m}\), a smooth parabolic curve opens downward, starting at \((0, 0)\), reaching a local maximum at \((1, 4)\), and passing through \((2, 0)\). A vertical dashed line extends from \((1, 4)\) down to 1 on the horizontal axis, and a horizontal dashed line extends from \((1, 4)\) left to 4 on the vertical axis. From \((2, 0)\) to \((4, -6)\), the graph is a straight solid line segment sloping downward. A vertical dashed line extends from \((4, -6)\) up to 4 on the horizontal axis, and a horizontal dashed line extends from \((4, -6)\) left to -6 on the vertical axis. From \((4, -6)\) to \((6, -6)\), the graph is a flat horizontal solid line. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604517-fZicua.jpg)

- **A.** The electric field is zero at \(x = 2\text{ m}\) because the electric potential is zero at that position, whereas the electric field is nonzero at \(x = 1\text{ m}\).
- **B.** In the interval \(0 < x < 1\text{ m}\), the electric field is directed in the \(+x\)-direction with an increasing magnitude because the potential increases toward its peak.
- **C.** The electric field is zero at \(x = 1\text{ m}\) and throughout the interval \(4\text{ m} < x < 6\text{ m}\), and has a constant component of \(E_x = +3\text{ V/m}\) throughout the interval \(2\text{ m} < x < 4\text{ m}\).
- **D.** In the interval \(2\text{ m} < x < 4\text{ m}\), the electric field has a constant component of \(E_x = -3\text{ V/m}\), and its magnitude is greatest in the interval \(4\text{ m} < x < 6\text{ m}\) where the potential is most negative.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124555/*