---
title: "A parallel-plate capacitor with plate area \\(A\\) has its plates initially separated by a distance \\(x_0\\). The magnitude of the attractive force between the plates is measured in two independent experiments as the plate separation is increased from \\(x_0\\) to \\(2x_0\\):  Experiment 1: The capacitor is charged to a net charge magnitude \\(Q_0\\) and then disconnected from the power supply, keeping the charge constant.  Experiment 2: The capacitor remains connected to a battery supplying a constant potential difference \\(V_0\\).  By what factor does the attractive force between the plates change (ratio \\(F_{\\text{final}} / F_{\\text{initial}}\\)) in Experiment 1 and Experiment 2?  | | Experiment 1 (Constant Charge \\(Q_0\\)) | Experiment 2 (Constant Voltage \\(V_0\\)) | |—|—|—| | (A) | \\(2\\) | \\(\\dfrac{1}{2}\\) | | (B) | \\(\\dfrac{1}{2}\\) | \\(\\dfrac{1}{4}\\) | | (C) | \\(1\\) | \\(\\dfrac{1}{4}\\) | | (D) | \\(\\dfrac{1}{4}\\) | \\(\\dfrac{1}{4}\\) |"
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/118322/"
date_modified: "2026-08-04T08:09:00+00:00"
---

# A parallel-plate capacitor with plate area \(A\) has its plates initially separated by a distance \(x_0\). The magnitude of the attractive force between the plates is measured in two independent experiments as the plate separation is increased from \(x_0\) to \(2x_0\):

Experiment 1: The capacitor is charged to a net charge magnitude \(Q_0\) and then disconnected from the power supply, keeping the charge constant.

Experiment 2: The capacitor remains connected to a battery supplying a constant potential difference \(V_0\).

By what factor does the attractive force between the plates change (ratio \(F_{\text{final}} / F_{\text{initial}}\)) in Experiment 1 and Experiment 2?

| | Experiment 1 (Constant Charge \(Q_0\)) | Experiment 2 (Constant Voltage \(V_0\)) |
|—|—|—|
| (A) | \(2\) | \(\dfrac{1}{2}\) |
| (B) | \(\dfrac{1}{2}\) | \(\dfrac{1}{4}\) |
| (C) | \(1\) | \(\dfrac{1}{4}\) |
| (D) | \(\dfrac{1}{4}\) | \(\dfrac{1}{4}\) |

A parallel-plate capacitor with plate area \(A\) has its plates initially separated by a distance \(x_0\). The magnitude of the attractive force between the plates is measured in two independent experiments as the plate separation is increased from \(x_0\) to \(2x_0\):

Experiment 1: The capacitor is charged to a net charge magnitude \(Q_0\) and then disconnected from the power supply, keeping the charge constant.

Experiment 2: The capacitor remains connected to a battery supplying a constant potential difference \(V_0\).

By what factor does the attractive force between the plates change (ratio \(F_{\text{final}} / F_{\text{initial}}\)) in Experiment 1 and Experiment 2?

| | Experiment 1 (Constant Charge \(Q_0\)) | Experiment 2 (Constant Voltage \(V_0\)) |
|---|---|---|
| (A) | \(2\) | \(\dfrac{1}{2}\) |
| (B) | \(\dfrac{1}{2}\) | \(\dfrac{1}{4}\) |
| (C) | \(1\) | \(\dfrac{1}{4}\) |
| (D) | \(\dfrac{1}{4}\) | \(\dfrac{1}{4}\) |

![A side-view schematic diagram of a parallel-plate capacitor oriented vertically. Two parallel flat conductive plates of vertical length L are separated by a horizontal gap x_0. The left plate contains three equally spaced plus signs on its inner face. The right plate contains three equally spaced minus signs on its inner face. A horizontal dimension line below the plates spans the distance between them and is labeled x_0. Thin straight lead wires extend horizontally outward from the outer faces of both plates. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830940-EXnwjf.jpg)

- **A.** (A)
- **B.** (B)
- **C.** (C)
- **D.** (D)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118322/*