---
title: "An ideal parallel-plate capacitor with plate area \\(A\\) and plate separation \\(d\\) has initial capacitance \\(C_0\\). A slab of uniform dielectric material with dielectric constant \\(\\kappa > 1\\) is inserted, completely filling the space between the plates.  Which of the following correctly pairs the new capacitance \\(C’\\) with the spatial distribution of the electric field magnitude \\(E\\) inside the dielectric region?"
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url: "https://nerd-notes.com/ubq/118180/"
date_modified: "2026-08-04T08:07:53+00:00"
---

# An ideal parallel-plate capacitor with plate area \(A\) and plate separation \(d\) has initial capacitance \(C_0\). A slab of uniform dielectric material with dielectric constant \(\kappa > 1\) is inserted, completely filling the space between the plates.

Which of the following correctly pairs the new capacitance \(C’\) with the spatial distribution of the electric field magnitude \(E\) inside the dielectric region?

An ideal parallel-plate capacitor with plate area \(A\) and plate separation \(d\) has initial capacitance \(C_0\). A slab of uniform dielectric material with dielectric constant \(\kappa > 1\) is inserted, completely filling the space between the plates.

Which of the following correctly pairs the new capacitance \(C'\) with the spatial distribution of the electric field magnitude \(E\) inside the dielectric region?

![A cross-sectional diagram of a parallel-plate capacitor. Two horizontal conducting plates of area A are oriented parallel to each other, separated by a vertical distance d. The upper plate has positive charges indicated on its inner surface, and the lower plate has negative charges indicated on its inner surface. The entire region between the plates is completely filled with a shaded rectangular dielectric slab labeled with dielectric constant \kappa. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830873-XUhtr4.jpg)

- **A.** Capacitance: \(C' = \kappa C_0\) | Electric field distribution: Uniform throughout the dielectric region
- **B.** Capacitance: \(C' = \kappa C_0\) | Electric field distribution: Decreases linearly from the positive plate to the negative plate
- **C.** Capacitance: \(C' = \dfrac{C_0}{\kappa}\) | Electric field distribution: Uniform throughout the dielectric region
- **D.** Capacitance: \(C' = \dfrac{C_0}{\kappa}\) | Electric field distribution: Decreases linearly from the positive plate to the negative plate

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118180/*