---
title: "An isolated solid conducting sphere of radius \\(R\\) initially carries a net positive charge \\(Q_0\\) and possesses electrostatic potential energy \\(U_0\\). A second uncharged solid conducting sphere of radius \\(3R\\) is placed a very large distance away. The two spheres are then connected by a long, thin conducting wire until electrostatic equilibrium is established. What are the final charge \\(Q_2\\) on the sphere of radius \\(3R\\) and the total final electrostatic potential energy \\(U_f\\) stored in the two-sphere system?"
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/121183/"
date_modified: "2026-08-23T04:58:27+00:00"
---

# An isolated solid conducting sphere of radius \(R\) initially carries a net positive charge \(Q_0\) and possesses electrostatic potential energy \(U_0\). A second uncharged solid conducting sphere of radius \(3R\) is placed a very large distance away. The two spheres are then connected by a long, thin conducting wire until electrostatic equilibrium is established. What are the final charge \(Q_2\) on the sphere of radius \(3R\) and the total final electrostatic potential energy \(U_f\) stored in the two-sphere system?

An isolated solid conducting sphere of radius \(R\) initially carries a net positive charge \(Q_0\) and possesses electrostatic potential energy \(U_0\). A second uncharged solid conducting sphere of radius \(3R\) is placed a very large distance away. The two spheres are then connected by a long, thin conducting wire until electrostatic equilibrium is established. What are the final charge \(Q_2\) on the sphere of radius \(3R\) and the total final electrostatic potential energy \(U_f\) stored in the two-sphere system?

![Two circular outlines representing spherical conductors are positioned side by side against a plain white background with a large horizontal gap between them. The left circle has a radius labeled R with a horizontal arrow from its center to its perimeter, and a label +Q_0 directly above it. The right circle is three times as large, with its radius labeled 3R with a horizontal arrow from its center to its perimeter. A single thin, continuous horizontal line connects the topmost point of the left circle to the topmost point of the right circle. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461107-iBf33G.jpg)

- **A.** \(Q_2 = \dfrac{1}{2}Q_0\) and \(U_f = \dfrac{1}{2}U_0\)
- **B.** \(Q_2 = \dfrac{3}{4}Q_0\) and \(U_f = \dfrac{1}{4}U_0\)
- **C.** \(Q_2 = \dfrac{1}{2}Q_0\) and \(U_f = \dfrac{1}{4}U_0\)
- **D.** \(Q_2 = \dfrac{3}{4}Q_0\) and \(U_f = \dfrac{3}{4}U_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121183/*