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title: "An isolated parallel-plate capacitor with square plates of side length \\(L\\) and plate separation \\(d\\) holds a fixed positive charge \\(Q\\). A dielectric slab with dielectric constant \\(\\kappa\\) and thickness \\(d\\) is inserted a distance \\(x\\) into the capacitor (\\(0 < x < L\\)). Let \\(C_0 = \\dfrac{\\varepsilon_0 L^2}{d}\\) be the capacitance of the empty capacitor. Which of the following expressions gives the magnitude of the electrostatic force exerted on the dielectric slab by the capacitor's electric field as a function of \\(x\\)?"
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url: "https://nerd-notes.com/ubq/118288/"
date_modified: "2026-08-04T08:08:42+00:00"
---

# An isolated parallel-plate capacitor with square plates of side length \(L\) and plate separation \(d\) holds a fixed positive charge \(Q\). A dielectric slab with dielectric constant \(\kappa\) and thickness \(d\) is inserted a distance \(x\) into the capacitor (\(0 < x < L\)). Let \(C_0 = \dfrac{\varepsilon_0 L^2}{d}\) be the capacitance of the empty capacitor. Which of the following expressions gives the magnitude of the electrostatic force exerted on the dielectric slab by the capacitor's electric field as a function of \(x\)?

An isolated parallel-plate capacitor with square plates of side length \(L\) and plate separation \(d\) holds a fixed positive charge \(Q\). A dielectric slab with dielectric constant \(\kappa\) and thickness \(d\) is inserted a distance \(x\) into the capacitor (\(0 < x < L\)). Let \(C_0 = \dfrac{\varepsilon_0 L^2}{d}\) be the capacitance of the empty capacitor. Which of the following expressions gives the magnitude of the electrostatic force exerted on the dielectric slab by the capacitor's electric field as a function of \(x\)?

![A side view of a parallel-plate capacitor with two horizontal parallel rectangular plates of length L separated vertically by distance d. A rectangular dielectric slab of length L and thickness d is partially inserted from the left between the plates to a distance x. The region of length x containing the dielectric is shaded gray. The remaining region of length L minus x between the plates is unshaded white space representing vacuum. A horizontal dashed coordinate axis x extends along the bottom plate, with origin x equals 0 at the left edge of the plates and x equals L at the right edge. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830921-qUP89d.jpg)

- **A.** \(\dfrac{Q^2 (\kappa - 1)}{2 C_0 L}\)
- **B.** \(\dfrac{Q^2 (\kappa - 1)}{2 C_0 L \left(1 + (\kappa - 1)\dfrac{x}{L}\right)}\)
- **C.** \(\dfrac{Q^2 \kappa}{2 C_0 L \left(1 + (\kappa - 1)\dfrac{x}{L}\right)^2}\)
- **D.** \(\dfrac{Q^2 (\kappa - 1)}{2 C_0 L \left(1 + (\kappa - 1)\dfrac{x}{L}\right)^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118288/*