---
title: "Three solid conducting spheres \\(A\\), \\(B\\), and \\(C\\) have radii \\(R_A = R\\), \\(R_B = 2R\\), and \\(R_C = 3R\\), respectively, and are located far from one another. The spheres are connected to each other by thin, long conducting wires, and a net positive charge \\(Q_0\\) is placed on the system. After the system reaches electrostatic equilibrium, which of the following correctly ranks the magnitude of the surface charge densities \\(\\sigma_A\\), \\(\\sigma_B\\), and \\(\\sigma_C\\) on the three spheres?"
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/118237/"
date_modified: "2026-08-04T08:08:20+00:00"
---

# Three solid conducting spheres \(A\), \(B\), and \(C\) have radii \(R_A = R\), \(R_B = 2R\), and \(R_C = 3R\), respectively, and are located far from one another. The spheres are connected to each other by thin, long conducting wires, and a net positive charge \(Q_0\) is placed on the system. After the system reaches electrostatic equilibrium, which of the following correctly ranks the magnitude of the surface charge densities \(\sigma_A\), \(\sigma_B\), and \(\sigma_C\) on the three spheres?

Three solid conducting spheres \(A\), \(B\), and \(C\) have radii \(R_A = R\), \(R_B = 2R\), and \(R_C = 3R\), respectively, and are located far from one another. The spheres are connected to each other by thin, long conducting wires, and a net positive charge \(Q_0\) is placed on the system. After the system reaches electrostatic equilibrium, which of the following correctly ranks the magnitude of the surface charge densities \(\sigma_A\), \(\sigma_B\), and \(\sigma_C\) on the three spheres?

![Three separated conducting spheres labeled A, B, and C are drawn from left to right. Sphere A is the smallest with radius R. Sphere B is in the middle with radius 2R. Sphere C is on the right with radius 3R. A thin horizontal line representing a conducting wire connects Sphere A to Sphere B, and another thin horizontal line connects Sphere B to Sphere C. Dashed radius lines extend from the center of each sphere to its boundary, labeled R, 2R, and 3R respectively. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830900-evc6wn.jpg)

- **A.** \(\sigma_A = \sigma_B = \sigma_C\)
- **B.** \(\sigma_C > \sigma_B > \sigma_A\)
- **C.** \(\sigma_B > \sigma_A > \sigma_C\)
- **D.** \(\sigma_A > \sigma_B > \sigma_C\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118237/*