---
title: "An isolated parallel-plate capacitor carries a uniform surface charge density of magnitude \\(\\sigma\\) on each plate. A dielectric slab with dielectric constant \\(\\kappa\\) is placed between and parallel to the plates, partially filling the space so that a dielectric layer and an adjacent vacuum layer coexist between the plates. What is the ratio of the electrostatic energy density within the dielectric layer to that within the vacuum layer, \\(u_{\\text{diel}} / u_{\\text{vac}}\\)?"
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url: "https://nerd-notes.com/ubq/124765/"
date_modified: "2026-09-28T14:11:08+00:00"
---

# An isolated parallel-plate capacitor carries a uniform surface charge density of magnitude \(\sigma\) on each plate. A dielectric slab with dielectric constant \(\kappa\) is placed between and parallel to the plates, partially filling the space so that a dielectric layer and an adjacent vacuum layer coexist between the plates. What is the ratio of the electrostatic energy density within the dielectric layer to that within the vacuum layer, \(u_{\text{diel}} / u_{\text{vac}}\)?

An isolated parallel-plate capacitor carries a uniform surface charge density of magnitude \(\sigma\) on each plate. A dielectric slab with dielectric constant \(\kappa\) is placed between and parallel to the plates, partially filling the space so that a dielectric layer and an adjacent vacuum layer coexist between the plates. What is the ratio of the electrostatic energy density within the dielectric layer to that within the vacuum layer, \(u_{\text{diel}} / u_{\text{vac}}\)?

![Two horizontal parallel lines represent capacitor plates, one at the top labeled with positive signs and one at the bottom labeled with negative signs. Between the plates, a horizontal rectangular region in the lower half is filled with light gray shading and labeled with the symbol \kappa. The remaining upper half between the shaded region and the top plate is unshaded white space labeled vacuum. A vertical dimension arrow on the left spans between the two plates and is labeled d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604668-OXksyB.jpg)

- **A.** \(\dfrac{1}{\kappa^2}\)
- **B.** \(\dfrac{1}{\kappa}\)
- **C.** \(1\)
- **D.** \(\kappa\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124765/*