---
title: "Two identical particles, each of mass \\(m\\) and positive charge \\(q\\), are free to move on a frictionless, insulating horizontal surface. Initially, the particles are separated by a very large distance, with one particle at rest and the other moving directly toward it at speed \\(v_0\\). What is the minimum separation distance between the two particles?"
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url: "https://nerd-notes.com/ubq/121055/"
date_modified: "2026-08-23T04:57:39+00:00"
---

# Two identical particles, each of mass \(m\) and positive charge \(q\), are free to move on a frictionless, insulating horizontal surface. Initially, the particles are separated by a very large distance, with one particle at rest and the other moving directly toward it at speed \(v_0\). What is the minimum separation distance between the two particles?

Two identical particles, each of mass \(m\) and positive charge \(q\), are free to move on a frictionless, insulating horizontal surface. Initially, the particles are separated by a very large distance, with one particle at rest and the other moving directly toward it at speed \(v_0\). What is the minimum separation distance between the two particles?

![Two small filled circles representing two identical particles of mass \(m\) and charge \(+q\) are aligned along a dashed horizontal line. The left particle has text \(m, +q\) above it and a single horizontal rightward arrow labeled \(v_0\) pointing toward the right particle. The right particle has text \(m, +q\) above it and text 'At rest' below it. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461058-MzjOlv.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121055/*