---
title: "An isolated parallel-plate capacitor with plate area \\(A\\) carries a constant charge of magnitude \\(Q_0\\) on each plate. A dielectric slab of dielectric constant \\(\\kappa > 1\\) initially fills the space between the plates. A closed Gaussian pillbox has one face inside the positive plate and the opposing face in the region between the plates within the dielectric, with side walls perpendicular to the plates. When the dielectric slab is completely withdrawn from the capacitor, how do the net electric flux through the Gaussian surface and the total electrostatic potential energy stored in the capacitor change?"
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url: "https://nerd-notes.com/ubq/124876/"
date_modified: "2026-09-28T14:11:46+00:00"
---

# An isolated parallel-plate capacitor with plate area \(A\) carries a constant charge of magnitude \(Q_0\) on each plate. A dielectric slab of dielectric constant \(\kappa > 1\) initially fills the space between the plates. A closed Gaussian pillbox has one face inside the positive plate and the opposing face in the region between the plates within the dielectric, with side walls perpendicular to the plates. When the dielectric slab is completely withdrawn from the capacitor, how do the net electric flux through the Gaussian surface and the total electrostatic potential energy stored in the capacitor change?

An isolated parallel-plate capacitor with plate area \(A\) carries a constant charge of magnitude \(Q_0\) on each plate. A dielectric slab of dielectric constant \(\kappa > 1\) initially fills the space between the plates. A closed Gaussian pillbox has one face inside the positive plate and the opposing face in the region between the plates within the dielectric, with side walls perpendicular to the plates. When the dielectric slab is completely withdrawn from the capacitor, how do the net electric flux through the Gaussian surface and the total electrostatic potential energy stored in the capacitor change?

![A side-view schematic of a parallel-plate capacitor. Two identical horizontal conducting plates of length L are separated by a vertical distance d. The upper plate has positive signs along its length and is labeled +Q_0. The lower plate has negative signs along its length and is labeled -Q_0. A shaded rectangular block representing a dielectric slab of dielectric constant \kappa completely fills the gap between the two plates. A small dashed cylinder oriented vertically represents a Gaussian pillbox; its top flat circular face lies entirely within the upper plate, its bottom flat circular face lies in the shaded dielectric region between the plates, and its vertical curved wall spans the boundary between the upper plate and the dielectric. A single horizontal arrow points to the right from the dielectric slab indicating its removal direction. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604705-O80hYG.jpg)

- **A.** Net electric flux: Remains unchanged ; Stored energy: Decreases
- **B.** Net electric flux: Remains unchanged ; Stored energy: Increases
- **C.** Net electric flux: Increases ; Stored energy: Decreases
- **D.** Net electric flux: Increases ; Stored energy: Increases

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124876/*