---
title: "Three thin, concentric, conducting spherical shells have radii \\(R\\), \\(2R\\), and \\(3R\\), and carry net charges \\(+q\\), \\(+2q\\), and \\(-3q\\), respectively, as shown. Assuming the electric potential is defined to be zero at infinity (\\(V(\\infty) = 0\\)), what is the electric potential \\(V\\) at the surface of the middle shell at a distance \\(r = 2R\\) from the center?"
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/118085/"
date_modified: "2026-08-04T08:05:03+00:00"
---

# Three thin, concentric, conducting spherical shells have radii \(R\), \(2R\), and \(3R\), and carry net charges \(+q\), \(+2q\), and \(-3q\), respectively, as shown. Assuming the electric potential is defined to be zero at infinity (\(V(\infty) = 0\)), what is the electric potential \(V\) at the surface of the middle shell at a distance \(r = 2R\) from the center?

Three thin, concentric, conducting spherical shells have radii \(R\), \(2R\), and \(3R\), and carry net charges \(+q\), \(+2q\), and \(-3q\), respectively, as shown. Assuming the electric potential is defined to be zero at infinity (\(V(\infty) = 0\)), what is the electric potential \(V\) at the surface of the middle shell at a distance \(r = 2R\) from the center?

![Three concentric thin black circles are centered at the origin of a white background. The innermost circle has radius R and is labeled +q. The middle circle has radius 2R and is labeled +2q. The outermost circle has radius 3R and is labeled -3q. A horizontal dashed line extends from the origin rightward through all three circles to indicate radial distance r, with tick marks at r = R, r = 2R, and r = 3R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830702-TsDCRo.jpg)

- **A.** \(\dfrac{q}{12\pi\varepsilon_0 R}\)
- **B.** \(\dfrac{q}{8\pi\varepsilon_0 R}\)
- **C.** \(\dfrac{q}{4\pi\varepsilon_0 R}\)
- **D.** \(\dfrac{3q}{8\pi\varepsilon_0 R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118085/*