---
title: "A thin, flat, circular insulating disk of radius \\(R\\) carries a total positive charge \\(Q\\) distributed uniformly over its surface. A small particle of mass \\(m\\) and positive charge \\(q\\) is launched from the center of the disk along its central perpendicular axis. Which of the following expressions represents the minimum launch speed \\(v_0\\) required for the particle to escape to an infinite distance from the disk?"
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url: "https://nerd-notes.com/ubq/118102/"
date_modified: "2026-08-04T08:05:08+00:00"
---

# A thin, flat, circular insulating disk of radius \(R\) carries a total positive charge \(Q\) distributed uniformly over its surface. A small particle of mass \(m\) and positive charge \(q\) is launched from the center of the disk along its central perpendicular axis. Which of the following expressions represents the minimum launch speed \(v_0\) required for the particle to escape to an infinite distance from the disk?

A thin, flat, circular insulating disk of radius \(R\) carries a total positive charge \(Q\) distributed uniformly over its surface. A small particle of mass \(m\) and positive charge \(q\) is launched from the center of the disk along its central perpendicular axis. Which of the following expressions represents the minimum launch speed \(v_0\) required for the particle to escape to an infinite distance from the disk?

![A thin circular disk of radius R lies horizontally in perspective view. The disk surface is light gray with a total charge label Q. A dashed vertical axis, labeled z, extends upward from the geometric center of the disk. A small particle labeled with charge q and mass m sits at the origin on the axis at the surface of the disk. An arrow labeled v_0 points straight up along the z-axis from the particle. A solid horizontal line segment extends from the center of the disk to its outer rim, labeled with radius R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830707-wZUFUp.jpg)

- **A.** \(v_0 = \sqrt{\dfrac{q Q}{4\pi \varepsilon_0 m R}}\)
- **B.** \(v_0 = \sqrt{\dfrac{q Q}{3\pi \varepsilon_0 m R}}\)
- **C.** \(v_0 = \sqrt{\dfrac{q Q}{2\pi \varepsilon_0 m R}}\)
- **D.** \(v_0 = \sqrt{\dfrac{q Q}{\pi \varepsilon_0 m R}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118102/*