---
title: "A system consists of a stationary point charge \\(+Q\\) fixed at the origin and an isolated, thin spherical conducting shell of radius \\(R\\) concentric with the point charge. The shell carries a net charge of \\(-2Q\\), and a tiny aperture in the shell allows particles to pass through without making electrical contact. A test particle of charge \\(+q_0\\) is moved radially outward from \\(r = \\dfrac{R}{2}\\) to \\(r = 2R\\). What is the work done by the electric field of the system on the test particle during this displacement?"
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url: "https://nerd-notes.com/ubq/124710/"
date_modified: "2026-09-28T14:09:13+00:00"
---

# A system consists of a stationary point charge \(+Q\) fixed at the origin and an isolated, thin spherical conducting shell of radius \(R\) concentric with the point charge. The shell carries a net charge of \(-2Q\), and a tiny aperture in the shell allows particles to pass through without making electrical contact. A test particle of charge \(+q_0\) is moved radially outward from \(r = \dfrac{R}{2}\) to \(r = 2R\). What is the work done by the electric field of the system on the test particle during this displacement?

A system consists of a stationary point charge \(+Q\) fixed at the origin and an isolated, thin spherical conducting shell of radius \(R\) concentric with the point charge. The shell carries a net charge of \(-2Q\), and a tiny aperture in the shell allows particles to pass through without making electrical contact. A test particle of charge \(+q_0\) is moved radially outward from \(r = \dfrac{R}{2}\) to \(r = 2R\). What is the work done by the electric field of the system on the test particle during this displacement?

![A cross-sectional diagram showing a central small filled circle labeled +Q at the center of a thin circular ring of radius R. A radial dashed line extends horizontally to the right from the center past the ring. On this dashed line, three positions are indicated: a point at r = R/2 labeled with a small open circle and +q_0, the intersection with the ring at r = R, and a point at r = 2R marked with a small dot. A single horizontal arrow points to the right from r = R/2 toward r = 2R. The ring is labeled with net charge -2Q near its top edge. A radial arrow points from the center toward the upper-right at 45 degrees to the ring with label R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604553-ntUcoR.jpg)

- **A.** \(-\dfrac{3Q q_0}{8\pi\varepsilon_0 R}\)
- **B.** \(-\dfrac{Q q_0}{8\pi\varepsilon_0 R}\)
- **C.** \(\dfrac{Q q_0}{8\pi\varepsilon_0 R}\)
- **D.** \(\dfrac{3Q q_0}{8\pi\varepsilon_0 R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124710/*