---
title: "A parallel-plate capacitor with plate separation \\(d\\) is charged by a battery so that the plates carry uniform surface charge densities \\(+\\sigma\\) and \\(-\\sigma\\), and is then disconnected from the battery. A dielectric slab of thickness \\(d/2\\) and dielectric constant \\(\\kappa = 2\\) is inserted into the center of the capacitor, occupying the region \\(d/4 \\le x \\le 3d/4\\), where \\(x = 0\\) is at the positively charged plate and \\(x = d\\) is at the negatively charged plate. Which of the following graphs best represents the magnitude of the net electric field \\(E\\) as a function of position \\(x\\) between the plates?"
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url: "https://nerd-notes.com/ubq/118318/"
date_modified: "2026-08-04T08:08:59+00:00"
---

# A parallel-plate capacitor with plate separation \(d\) is charged by a battery so that the plates carry uniform surface charge densities \(+\sigma\) and \(-\sigma\), and is then disconnected from the battery. A dielectric slab of thickness \(d/2\) and dielectric constant \(\kappa = 2\) is inserted into the center of the capacitor, occupying the region \(d/4 \le x \le 3d/4\), where \(x = 0\) is at the positively charged plate and \(x = d\) is at the negatively charged plate. Which of the following graphs best represents the magnitude of the net electric field \(E\) as a function of position \(x\) between the plates?

A parallel-plate capacitor with plate separation \(d\) is charged by a battery so that the plates carry uniform surface charge densities \(+\sigma\) and \(-\sigma\), and is then disconnected from the battery. A dielectric slab of thickness \(d/2\) and dielectric constant \(\kappa = 2\) is inserted into the center of the capacitor, occupying the region \(d/4 \le x \le 3d/4\), where \(x = 0\) is at the positively charged plate and \(x = d\) is at the negatively charged plate. Which of the following graphs best represents the magnitude of the net electric field \(E\) as a function of position \(x\) between the plates?

![A side view of a parallel-plate capacitor in the xy-plane. A tall vertical line at x = 0 represents the left plate, labeled with surface charge density +\sigma. A tall vertical line at x = d represents the right plate, labeled with surface charge density -\sigma. Between the plates, a shaded rectangle of width d/2 represents a dielectric slab located from x = d/4 to x = 3d/4, labeled \kappa = 2. Below the plates, a horizontal x-axis extends from x = 0 to x = d, with tick marks indicating x = 0, x = d/4, x = 3d/4, and x = d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830938-w58fOi.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118318/*