---
title: "A parallel-plate capacitor with rectangular plates of length \\(L\\), width \\(w\\), and plate separation \\(d\\) is connected to a battery that maintains a constant potential difference \\(V_0\\). A dielectric slab with dielectric constant \\(\\kappa\\) and thickness \\(d\\) is partially inserted a distance \\(x\\) between the plates, where \\(0 < x < L\\). Which of the following expressions represents the magnitude of the electrostatic force exerted on the dielectric slab by the electric field?"
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url: "https://nerd-notes.com/ubq/121121/"
date_modified: "2026-08-23T04:58:10+00:00"
---

# A parallel-plate capacitor with rectangular plates of length \(L\), width \(w\), and plate separation \(d\) is connected to a battery that maintains a constant potential difference \(V_0\). A dielectric slab with dielectric constant \(\kappa\) and thickness \(d\) is partially inserted a distance \(x\) between the plates, where \(0 < x < L\). Which of the following expressions represents the magnitude of the electrostatic force exerted on the dielectric slab by the electric field?

A parallel-plate capacitor with rectangular plates of length \(L\), width \(w\), and plate separation \(d\) is connected to a battery that maintains a constant potential difference \(V_0\). A dielectric slab with dielectric constant \(\kappa\) and thickness \(d\) is partially inserted a distance \(x\) between the plates, where \(0 < x < L\). Which of the following expressions represents the magnitude of the electrostatic force exerted on the dielectric slab by the electric field?

![A side-perspective schematic of a parallel-plate capacitor and a dielectric slab. Two horizontal rectangular conducting plates of length \(L\) and separation \(d\) are shown parallel to each other. A battery maintaining a potential difference labeled \(V_0\) is connected across the two plates via thin conducting wires. A shaded rectangular dielectric slab of thickness \(d\) is partially inserted from the left between the plates by a distance labeled \(x\). A double-headed horizontal arrow indicates the inserted distance \(x\), and another horizontal dimension line along the top plate indicates the total length \(L\). A vertical dimension arrow between the two plates indicates the plate separation \(d\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461090-nj0OD7.jpg)

- **A.** \(\dfrac{\varepsilon_0 w \kappa V_0^2}{2d}\)
- **B.** \(\dfrac{\varepsilon_0 w \kappa V_0^2}{d}\)
- **C.** \(\dfrac{\varepsilon_0 w (\kappa - 1) V_0^2}{d}\)
- **D.** \(\dfrac{\varepsilon_0 w (\kappa - 1) V_0^2}{2d}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121121/*