---
title: "Three thin, concentric, conducting spherical shells have radii \\(R\\), \\(2R\\), and \\(3R\\). The innermost shell carries a net charge \\(+Q\\), the outermost shell carries a net charge \\(-Q\\), and the middle shell is connected to ground so that its electric potential is zero. Expressed in terms of Coulomb’s constant \\(k = \\dfrac{1}{4\\pi\\varepsilon_0}\\), \\(Q\\), and \\(R\\), what is the total electrostatic potential energy stored in this 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/118132/"
date_modified: "2026-08-04T08:05:22+00:00"
---

# Three thin, concentric, conducting spherical shells have radii \(R\), \(2R\), and \(3R\). The innermost shell carries a net charge \(+Q\), the outermost shell carries a net charge \(-Q\), and the middle shell is connected to ground so that its electric potential is zero. Expressed in terms of Coulomb’s constant \(k = \dfrac{1}{4\pi\varepsilon_0}\), \(Q\), and \(R\), what is the total electrostatic potential energy stored in this system?

Three thin, concentric, conducting spherical shells have radii \(R\), \(2R\), and \(3R\). The innermost shell carries a net charge \(+Q\), the outermost shell carries a net charge \(-Q\), and the middle shell is connected to ground so that its electric potential is zero. Expressed in terms of Coulomb's constant \(k = \dfrac{1}{4\pi\varepsilon_0}\), \(Q\), and \(R\), what is the total electrostatic potential energy stored in this system?

![Three concentric circles representing thin spherical shells in cross-section. The innermost circle has radius R and is labeled +Q. The middle circle has radius 2R and has a wire extending outward to a standard ground symbol consisting of three horizontal lines of decreasing length. The outermost circle has radius 3R and is labeled -Q. Radial dashed line segments extend from the common center to each shell, 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-1-1785830722-10eW8y.jpg)

- **A.** \(\dfrac{k Q^2}{4 R}\)
- **B.** \(\dfrac{11 k Q^2}{36 R}\)
- **C.** \(\dfrac{k Q^2}{3 R}\)
- **D.** \(\dfrac{11 k Q^2}{18 R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118132/*