---
title: "Two isolated conducting spheres, Sphere 1 of radius \\(R\\) and Sphere 2 of radius \\(2R\\), are connected by a long, thin conducting wire. A total net charge \\(Q_0\\) is placed on the system, and charge redistributes until electrostatic equilibrium is established. Which of the following correctly gives the ratio of the electrostatic potentials at their surfaces, \\(V_1 / V_2\\), and the ratio of the net charges on the spheres, \\(Q_1 / Q_2\\)?"
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/118187/"
date_modified: "2026-08-04T08:07:57+00:00"
---

# Two isolated conducting spheres, Sphere 1 of radius \(R\) and Sphere 2 of radius \(2R\), are connected by a long, thin conducting wire. A total net charge \(Q_0\) is placed on the system, and charge redistributes until electrostatic equilibrium is established. Which of the following correctly gives the ratio of the electrostatic potentials at their surfaces, \(V_1 / V_2\), and the ratio of the net charges on the spheres, \(Q_1 / Q_2\)?

Two isolated conducting spheres, Sphere 1 of radius \(R\) and Sphere 2 of radius \(2R\), are connected by a long, thin conducting wire. A total net charge \(Q_0\) is placed on the system, and charge redistributes until electrostatic equilibrium is established. Which of the following correctly gives the ratio of the electrostatic potentials at their surfaces, \(V_1 / V_2\), and the ratio of the net charges on the spheres, \(Q_1 / Q_2\)?

![A schematic diagram showing two conducting spheres, labeled Sphere 1 and Sphere 2, separated horizontally and connected by a thin horizontal wire. Sphere 1 on the left is smaller with radius R, and Sphere 2 on the right is larger with radius 2R. Both spheres are rendered as shaded circles. A thin straight horizontal wire connects the top of the two spheres. No other text or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830877-a6WtKk.jpg)

- **A.** \(V_1 / V_2 = 1/2\) and \(Q_1 / Q_2 = 1/2\)
- **B.** \(V_1 / V_2 = 1/2\) and \(Q_1 / Q_2 = 1\)
- **C.** \(V_1 / V_2 = 1\) and \(Q_1 / Q_2 = 1/2\)
- **D.** \(V_1 / V_2 = 1\) and \(Q_1 / Q_2 = 2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118187/*