---
title: "In a region of space along the \\(x\\)-axis, the electric potential as a function of position \\(x\\) is described by \\(V(x) = V_0 \\left( \\dfrac{x^3}{x_0^3} – \\dfrac{3x}{x_0} \\right)\\), where \\(V_0\\) and \\(x_0\\) are positive constants. Which of the following expressions represents the \\(x\\)-component of the electric field, \\(E_x(x)\\), as a function of \\(x\\)?"
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url: "https://nerd-notes.com/ubq/118094/"
date_modified: "2026-08-04T08:05:04+00:00"
---

# In a region of space along the \(x\)-axis, the electric potential as a function of position \(x\) is described by \(V(x) = V_0 \left( \dfrac{x^3}{x_0^3} – \dfrac{3x}{x_0} \right)\), where \(V_0\) and \(x_0\) are positive constants. Which of the following expressions represents the \(x\)-component of the electric field, \(E_x(x)\), as a function of \(x\)?

In a region of space along the \(x\)-axis, the electric potential as a function of position \(x\) is described by \(V(x) = V_0 \left( \dfrac{x^3}{x_0^3} - \dfrac{3x}{x_0} \right)\), where \(V_0\) and \(x_0\) are positive constants. Which of the following expressions represents the \(x\)-component of the electric field, \(E_x(x)\), as a function of \(x\)?

- **A.** \(\dfrac{3V_0}{x_0}\left(1 - \dfrac{x^2}{x_0^2}\right)\)
- **B.** \(\dfrac{3V_0}{x_0}\left(\dfrac{x^2}{x_0^2} - 1\right)\)
- **C.** \(\dfrac{V_0}{x_0}\left(3 - \dfrac{x^2}{x_0^2}\right)\)
- **D.** \(\dfrac{3V_0}{x_0}\left(1 - \dfrac{x^3}{x_0^3}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118094/*