---
title: "Three large dielectric slabs, labeled \\(1\\), \\(2\\), and \\(3\\), are placed one at a time into the same uniform external electric field of magnitude \\(E_0\\). The faces of each slab are oriented perpendicular to the field lines. The dielectric constants of the slabs are \\(\\kappa_1 = 2\\), \\(\\kappa_2 = 4\\), and \\(\\kappa_3 = 6\\), respectively. Which of the following correctly ranks the magnitude of the induced surface charge density \\(\\sigma_{\\text{ind}}\\) on the faces of the slabs?"
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url: "https://nerd-notes.com/ubq/121130/"
date_modified: "2026-08-23T04:58:14+00:00"
---

# Three large dielectric slabs, labeled \(1\), \(2\), and \(3\), are placed one at a time into the same uniform external electric field of magnitude \(E_0\). The faces of each slab are oriented perpendicular to the field lines. The dielectric constants of the slabs are \(\kappa_1 = 2\), \(\kappa_2 = 4\), and \(\kappa_3 = 6\), respectively. Which of the following correctly ranks the magnitude of the induced surface charge density \(\sigma_{\text{ind}}\) on the faces of the slabs?

Three large dielectric slabs, labeled \(1\), \(2\), and \(3\), are placed one at a time into the same uniform external electric field of magnitude \(E_0\). The faces of each slab are oriented perpendicular to the field lines. The dielectric constants of the slabs are \(\kappa_1 = 2\), \(\kappa_2 = 4\), and \(\kappa_3 = 6\), respectively. Which of the following correctly ranks the magnitude of the induced surface charge density \(\sigma_{\text{ind}}\) on the faces of the slabs?

![A rectangular dielectric slab viewed in cross-section with its flat faces oriented vertically. Three horizontal, rightward-pointing parallel arrows labeled E_0 enter from the left and exit to the right. Inside the slab, the left vertical surface contains a vertical column of five evenly spaced minus signs, and the right vertical surface contains a vertical column of five evenly spaced plus signs. A label \kappa sits at the center of the slab. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461094-qeZpXa.jpg)

- **A.** \(\sigma_{\text{ind},3} > \sigma_{\text{ind},2} > \sigma_{\text{ind},1}\)
- **B.** \(\sigma_{\text{ind},1} > \sigma_{\text{ind},2} > \sigma_{\text{ind},3}\)
- **C.** \(\sigma_{\text{ind},1} = \sigma_{\text{ind},2} = \sigma_{\text{ind},3}\)
- **D.** \(\sigma_{\text{ind},2} > \sigma_{\text{ind},1} > \sigma_{\text{ind},3}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121130/*