---
title: "An electric field directed along the \\(x\\)-axis has a constant value \\(E_x = +E_0\\) in the region \\(0 < x < d\\) and a constant value \\(E_x = -E_0\\) in the region \\(d < x < 2d\\), where \\(E_0\\) and \\(d\\) are positive constants. The electric potential is defined to be zero at \\(x = 0\\). Which of the following graphs best represents the electric potential \\(V(x)\\) as a function of position \\(x\\) from \\(x = 0\\) to \\(x = 2d\\)?"
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/118078/"
date_modified: "2026-08-04T08:05:00+00:00"
---

# An electric field directed along the \(x\)-axis has a constant value \(E_x = +E_0\) in the region \(0 < x < d\) and a constant value \(E_x = -E_0\) in the region \(d < x < 2d\), where \(E_0\) and \(d\) are positive constants. The electric potential is defined to be zero at \(x = 0\). Which of the following graphs best represents the electric potential \(V(x)\) as a function of position \(x\) from \(x = 0\) to \(x = 2d\)?

An electric field directed along the \(x\)-axis has a constant value \(E_x = +E_0\) in the region \(0 < x < d\) and a constant value \(E_x = -E_0\) in the region \(d < x < 2d\), where \(E_0\) and \(d\) are positive constants. The electric potential is defined to be zero at \(x = 0\). Which of the following graphs best represents the electric potential \(V(x)\) as a function of position \(x\) from \(x = 0\) to \(x = 2d\)?

- **A.** A graph that increases linearly from \(V = 0\) at \(x = 0\) to \(V = +E_0 d\) at \(x = d\), and then decreases linearly to \(V = 0\) at \(x = 2d\).
- **B.** A graph that is constant at \(V = -E_0 d\) for \(0 < x < d\), jumps abruptly at \(x = d\), and is constant at \(V = +E_0 d\) for \(d < x < 2d\).
- **C.** A graph that decreases linearly from \(V = 0\) at \(x = 0\) to \(V = -E_0 d\) at \(x = d\), and then increases linearly to \(V = 0\) at \(x = 2d\).
- **D.** A graph that decreases linearly from \(V = 0\) at \(x = 0\) to \(V = -E_0 d\) at \(x = d\), and then continues decreasing linearly with the same slope to \(V = -2E_0 d\) at \(x = 2d\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118078/*