---
title: "A parallel-plate capacitor consists of two large conducting plates of area \\(A\\) separated by a distance \\(d\\) in vacuum at positions \\(x = 0\\) and \\(x = d\\).  The capacitor is charged so that the plates carry fixed free charges \\(+Q\\) at \\(x = 0\\) and \\(-Q\\) at \\(x = d\\), after which it is isolated from the charging source.  An uncharged dielectric slab of thickness \\(d/2\\) and dielectric constant \\(\\kappa > 1\\) is inserted between the plates, centered at \\(x = d/2\\) so that it occupies the region \\(d/4 \\le x \\le 3d/4\\).  Neglecting edge effects, which of the following graphs best represents the magnitude of the electric field \\(E\\) as a function of position \\(x\\) between the plates, from \\(x = 0\\) to \\(x = d\\)?"
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url: "https://nerd-notes.com/ubq/124968/"
date_modified: "2026-09-28T14:12:18+00:00"
---

# A parallel-plate capacitor consists of two large conducting plates of area \(A\) separated by a distance \(d\) in vacuum at positions \(x = 0\) and \(x = d\).

The capacitor is charged so that the plates carry fixed free charges \(+Q\) at \(x = 0\) and \(-Q\) at \(x = d\), after which it is isolated from the charging source.

An uncharged dielectric slab of thickness \(d/2\) and dielectric constant \(\kappa > 1\) is inserted between the plates, centered at \(x = d/2\) so that it occupies the region \(d/4 \le x \le 3d/4\).

Neglecting edge effects, which of the following graphs best represents the magnitude of the electric field \(E\) as a function of position \(x\) between the plates, from \(x = 0\) to \(x = d\)?

A parallel-plate capacitor consists of two large conducting plates of area \(A\) separated by a distance \(d\) in vacuum at positions \(x = 0\) and \(x = d\).

The capacitor is charged so that the plates carry fixed free charges \(+Q\) at \(x = 0\) and \(-Q\) at \(x = d\), after which it is isolated from the charging source.

An uncharged dielectric slab of thickness \(d/2\) and dielectric constant \(\kappa > 1\) is inserted between the plates, centered at \(x = d/2\) so that it occupies the region \(d/4 \le x \le 3d/4\).

Neglecting edge effects, which of the following graphs best represents the magnitude of the electric field \(E\) as a function of position \(x\) between the plates, from \(x = 0\) to \(x = d\)?

![A schematic diagram showing a parallel-plate capacitor along a horizontal coordinate axis labeled x with an arrowhead pointing right. Two identical vertical black rectangles represent the capacitor plates, one located at x = 0 labeled +Q above its top edge, and one at x = d labeled -Q above its top edge. Centered between the plates is a light-gray shaded rectangle representing a dielectric slab, spanning horizontally from x = d/4 to x = 3d/4 and vertically matching the height of the plates, labeled \kappa at its center. The regions between x = 0 and x = d/4, and between x = 3d/4 and x = d, are unshaded white space. Four vertical tick marks on the horizontal axis indicate positions 0, d/4, 3d/4, and d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604736-xJusfn.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/124968/*