---
title: "An ideal parallel-plate capacitor with plate separation \\(d\\) is connected to a battery that maintains a constant potential difference \\(V_0\\). A slab of linear dielectric material with dielectric constant \\(\\kappa > 1\\) is slowly inserted between the plates until it completely fills the space. Two students disagree on the outcome: one asserts that dielectric polarization must reduce the net electric field between the plates, while the other asserts that the net electric field cannot change because the potential difference and plate separation remain fixed. Which of the following explanations correctly resolves this apparent contradiction?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/124793/"
date_modified: "2026-09-28T14:11:18+00:00"
---

# An ideal parallel-plate capacitor with plate separation \(d\) is connected to a battery that maintains a constant potential difference \(V_0\). A slab of linear dielectric material with dielectric constant \(\kappa > 1\) is slowly inserted between the plates until it completely fills the space. Two students disagree on the outcome: one asserts that dielectric polarization must reduce the net electric field between the plates, while the other asserts that the net electric field cannot change because the potential difference and plate separation remain fixed. Which of the following explanations correctly resolves this apparent contradiction?

An ideal parallel-plate capacitor with plate separation \(d\) is connected to a battery that maintains a constant potential difference \(V_0\). A slab of linear dielectric material with dielectric constant \(\kappa > 1\) is slowly inserted between the plates until it completely fills the space. Two students disagree on the outcome: one asserts that dielectric polarization must reduce the net electric field between the plates, while the other asserts that the net electric field cannot change because the potential difference and plate separation remain fixed. Which of the following explanations correctly resolves this apparent contradiction?

![A schematic diagram showing a parallel-plate capacitor connected to a DC voltage source. Two horizontal parallel lines of equal length represent the conducting plates separated by a vertical distance \(d\). A shaded rectangular block fills the entire region between the top and bottom plates, labeled with the symbol \(\kappa\). Conducting wire lines extend from the top and bottom plates to the terminals of a battery symbol on the left, labeled with the potential difference \(V_0\). A vertical double-headed arrow spanning between the inner faces of the plates is labeled \(d\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604678-nTmWna.jpg)

- **A.** The battery prevents bound charges from accumulating on the dielectric surfaces by continuously neutralizing them with conduction current, which prevents an opposing internal field from forming and keeps the net electric field equal to \(V_0 / d\).
- **B.** The polarization reduces the net electric field inside the dielectric material to \(V_0 / (\kappa d)\), because the path integral relationship \(\Delta V = \int \vec{E} \cdot d\vec{\ell}\) is replaced by \(\Delta V = \int \vec{D} \cdot d\vec{\ell}\) in the presence of a dielectric medium.
- **C.** The dielectric polarization momentarily weakens the internal field, which causes the battery to remove free charge from the plates until the free surface charge matches the bound surface charge and restores the field to its initial value.
- **D.** The dielectric develops bound surface charges that produce an opposing electric field, but the battery supplies additional free charge to the plates, increasing the free-charge field by an amount that exactly offsets the polarization field and maintains the net electric field at \(V_0 / d\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124793/*