---
title: "A solid insulating sphere of radius \\(R\\) has a total electric charge \\(Q\\) distributed uniformly throughout its volume. The sphere is assembled by bringing infinitesimally thin spherical shells of charge from infinity and adding them layer by layer until the full sphere of radius \\(R\\) is formed. In terms of \\(Q\\), \\(R\\), and physical constants, what is the total electrostatic potential energy stored in the assembled sphere?"
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url: "https://nerd-notes.com/ubq/121062/"
date_modified: "2026-08-23T04:57:40+00:00"
---

# A solid insulating sphere of radius \(R\) has a total electric charge \(Q\) distributed uniformly throughout its volume. The sphere is assembled by bringing infinitesimally thin spherical shells of charge from infinity and adding them layer by layer until the full sphere of radius \(R\) is formed. In terms of \(Q\), \(R\), and physical constants, what is the total electrostatic potential energy stored in the assembled sphere?

A solid insulating sphere of radius \(R\) has a total electric charge \(Q\) distributed uniformly throughout its volume. The sphere is assembled by bringing infinitesimally thin spherical shells of charge from infinity and adding them layer by layer until the full sphere of radius \(R\) is formed. In terms of \(Q\), \(R\), and physical constants, what is the total electrostatic potential energy stored in the assembled sphere?

![A cross-sectional diagram of a solid sphere of radius \(R\) centered at the origin. An inner concentric shaded circular region of radius \(r\) represents the charge already assembled, with a solid line arrow labeled \(r\) pointing from the center toward the upper-right at 45 degrees to the outer edge of this inner region. Immediately surrounding the inner region is an infinitesimally thin concentric annular shell of thickness labeled \(dr\). A solid line arrow labeled \(R\) extends from the center toward the upper-left at 135 degrees to the outer boundary of the entire sphere. A curved dashed arrow labeled \(dq\) starts outside the outer boundary on the right and points inward toward the annular shell of thickness \(dr\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461060-qasNI7.jpg)

- **A.** \(\dfrac{3Q^2}{20\pi\varepsilon_0 R}\)
- **B.** \(\dfrac{Q^2}{8\pi\varepsilon_0 R}\)
- **C.** \(\dfrac{3Q^2}{8\pi\varepsilon_0 R}\)
- **D.** \(\dfrac{Q^2}{4\pi\varepsilon_0 R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121062/*