---
title: "A small particle with mass \\(m\\) and positive charge \\(q\\) is projected from a very large distance directly toward a fixed, stationary point charge also with positive charge \\(q\\). The initial speed of the moving particle when far away from the fixed charge is \\(v_0\\). Electrostatic forces dominate all other interactions in this system. Which of the following expressions correctly represents the distance of closest approach \\(r_{\\text{min}}\\) between the two charges?"
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url: "https://nerd-notes.com/ubq/118050/"
date_modified: "2026-08-04T08:04:53+00:00"
---

# A small particle with mass \(m\) and positive charge \(q\) is projected from a very large distance directly toward a fixed, stationary point charge also with positive charge \(q\). The initial speed of the moving particle when far away from the fixed charge is \(v_0\). Electrostatic forces dominate all other interactions in this system. Which of the following expressions correctly represents the distance of closest approach \(r_{\text{min}}\) between the two charges?

A small particle with mass \(m\) and positive charge \(q\) is projected from a very large distance directly toward a fixed, stationary point charge also with positive charge \(q\). The initial speed of the moving particle when far away from the fixed charge is \(v_0\). Electrostatic forces dominate all other interactions in this system. Which of the following expressions correctly represents the distance of closest approach \(r_{\text{min}}\) between the two charges?

![A horizontal axis showing two positive point charges. On the far right, a fixed circle labeled +q is stationary. Far to the left, a second circle labeled +q with mass m is moving to the right, indicated by a horizontal arrow labeled v_0 pointing toward the fixed charge. A dashed line indicates the straight trajectory between them.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830693-96KY8o.jpg)

- **A.** \(\dfrac{q^2}{2\pi\varepsilon_0 m v_0^2}\)
- **B.** \(\dfrac{q^2}{4\pi\varepsilon_0 m v_0^2}\)
- **C.** \(\dfrac{q^2}{\pi\varepsilon_0 m v_0^2}\)
- **D.** \(\dfrac{q^2}{8\pi\varepsilon_0 m v_0^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118050/*