---
title: "A parallel-plate capacitor with fixed plate area \\(A\\) and adjustable plate separation \\(d\\) is filled with an insulating material of dielectric constant \\(\\kappa\\) and dielectric breakdown strength \\(E_{\\text{max}}\\). The breakdown strength represents the maximum electric field magnitude the dielectric can withstand before conducting. For any chosen separation \\(d\\), the capacitor is charged to the maximum potential difference \\(V_{\\text{max}}\\) it can sustain without exceeding \\(E_{\\text{max}}\\). In the limit as the plate separation approaches zero (\\(d \\to 0\\)), which of the following correctly describes the behavior of the maximum stored charge \\(Q_{\\text{max}}\\) and the maximum stored electrostatic potential energy \\(U_{\\text{max}}\\)?"
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url: "https://nerd-notes.com/ubq/121191/"
date_modified: "2026-08-23T04:58:37+00:00"
---

# A parallel-plate capacitor with fixed plate area \(A\) and adjustable plate separation \(d\) is filled with an insulating material of dielectric constant \(\kappa\) and dielectric breakdown strength \(E_{\text{max}}\). The breakdown strength represents the maximum electric field magnitude the dielectric can withstand before conducting. For any chosen separation \(d\), the capacitor is charged to the maximum potential difference \(V_{\text{max}}\) it can sustain without exceeding \(E_{\text{max}}\). In the limit as the plate separation approaches zero (\(d \to 0\)), which of the following correctly describes the behavior of the maximum stored charge \(Q_{\text{max}}\) and the maximum stored electrostatic potential energy \(U_{\text{max}}\)?

A parallel-plate capacitor with fixed plate area \(A\) and adjustable plate separation \(d\) is filled with an insulating material of dielectric constant \(\kappa\) and dielectric breakdown strength \(E_{\text{max}}\). The breakdown strength represents the maximum electric field magnitude the dielectric can withstand before conducting. For any chosen separation \(d\), the capacitor is charged to the maximum potential difference \(V_{\text{max}}\) it can sustain without exceeding \(E_{\text{max}}\). In the limit as the plate separation approaches zero (\(d \to 0\)), which of the following correctly describes the behavior of the maximum stored charge \(Q_{\text{max}}\) and the maximum stored electrostatic potential energy \(U_{\text{max}}\)?

![A side cross-sectional schematic of a parallel-plate capacitor oriented horizontally. Two thick horizontal lines of equal length represent the conductive plates, each with area labeled \(A\). The upper plate is at the top, and the lower plate is at the bottom, separated by a vertical distance labeled \(d\) with a double-headed vertical dimension arrow between them. The entire space between the plates is shaded with uniform light gray diagonal hatching representing a dielectric material labeled with dielectric constant \(\kappa\) and breakdown field \(E_{\text{max}}\). Exactly three vertical downward-pointing arrows are evenly spaced within the dielectric region between the plates, labeled \(\vec{E}\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461117-alqW6B.jpg)

- **A.** \(Q_{\text{max}}\) approaches infinity, and \(U_{\text{max}}\) approaches infinity.
- **B.** \(Q_{\text{max}}\) approaches a constant nonzero value, and \(U_{\text{max}}\) approaches zero.
- **C.** \(Q_{\text{max}}\) approaches a constant nonzero value, and \(U_{\text{max}}\) approaches infinity.
- **D.** \(Q_{\text{max}}\) approaches zero, and \(U_{\text{max}}\) approaches zero.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121191/*