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title: "A parallel-plate capacitor with plate separation \\(d\\) has its left plate at position \\(x = 0\\) held at electric potential \\(V(0) = V_0\\) and its right plate at \\(x = d\\) grounded at \\(V(d) = 0\\). A slab of dielectric material with dielectric constant \\(\\kappa > 1\\) and thickness \\(d/2\\) is inserted into the center of the capacitor, occupying the region \\(d/4 \\le x \\le 3d/4\\). Which graph best represents the electric potential \\(V(x)\\) as a function of position \\(x\\) between the plates?"
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url: "https://nerd-notes.com/ubq/118308/"
date_modified: "2026-08-04T08:08:55+00:00"
---

# A parallel-plate capacitor with plate separation \(d\) has its left plate at position \(x = 0\) held at electric potential \(V(0) = V_0\) and its right plate at \(x = d\) grounded at \(V(d) = 0\). A slab of dielectric material with dielectric constant \(\kappa > 1\) and thickness \(d/2\) is inserted into the center of the capacitor, occupying the region \(d/4 \le x \le 3d/4\). Which graph best represents the electric potential \(V(x)\) as a function of position \(x\) between the plates?

A parallel-plate capacitor with plate separation \(d\) has its left plate at position \(x = 0\) held at electric potential \(V(0) = V_0\) and its right plate at \(x = d\) grounded at \(V(d) = 0\). A slab of dielectric material with dielectric constant \(\kappa > 1\) and thickness \(d/2\) is inserted into the center of the capacitor, occupying the region \(d/4 \le x \le 3d/4\). Which graph best represents the electric potential \(V(x)\) as a function of position \(x\) between the plates?

![A cross-sectional view of a parallel-plate capacitor with plates oriented vertically. The left plate is at horizontal position x = 0 and is labeled V_0. The right plate is at horizontal position x = d and is labeled 0. Between the plates, from x = d/4 to x = 3d/4, there is a shaded rectangular slab representing a dielectric material with dielectric constant kappa > 1. The regions from x = 0 to x = d/4 and from x = 3d/4 to x = d are unshaded, representing vacuum. Below the plates, a horizontal x-axis is drawn with tick marks at 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-1-1785830933-kSk9VY.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/118308/*