---
title: "A thin, flexible, non-conducting spherical shell of initial radius \\(R\\) carries a total charge \\(Q\\) distributed uniformly over its surface. An external mechanism allows the shell to expand radially to a final radius of \\(\\dfrac{3}{2}R\\). Which of the following expressions represents the total work done by the electrostatic forces on the shell during this expansion?"
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url: "https://nerd-notes.com/ubq/118176/"
date_modified: "2026-08-04T08:06:03+00:00"
---

# A thin, flexible, non-conducting spherical shell of initial radius \(R\) carries a total charge \(Q\) distributed uniformly over its surface. An external mechanism allows the shell to expand radially to a final radius of \(\dfrac{3}{2}R\). Which of the following expressions represents the total work done by the electrostatic forces on the shell during this expansion?

A thin, flexible, non-conducting spherical shell of initial radius \(R\) carries a total charge \(Q\) distributed uniformly over its surface. An external mechanism allows the shell to expand radially to a final radius of \(\dfrac{3}{2}R\). Which of the following expressions represents the total work done by the electrostatic forces on the shell during this expansion?

![A two-dimensional cross-sectional diagram showing two concentric dashed and solid circles representing a spherical shell. The inner circle is solid with radius labeled R, extending from the center to the edge of the inner circle with a single-headed arrow. The outer circle is dashed with a radius arrow extending from the center to the outer circle, labeled 1.5R. Small positive plus signs (+) are distributed uniformly around the perimeter of the inner solid circle. Four small outward-pointing arrows are spaced evenly around the outer circle, indicating radial expansion. The center point is marked with a small black dot. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830763-CMPOrv.jpg)

- **A.** \(\dfrac{Q^2}{12\pi\varepsilon_0 R}\)
- **B.** \(\dfrac{Q^2}{16\pi\varepsilon_0 R}\)
- **C.** \(\dfrac{Q^2}{18\pi\varepsilon_0 R}\)
- **D.** \(\dfrac{Q^2}{24\pi\varepsilon_0 R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118176/*