---
title: "An uncharged, solid, spherical conducting shell has an inner radius \\(R_1\\) and an outer radius \\(R_2\\). A small positive point charge \\(+Q\\) is placed inside the cavity of the shell at a distance \\(d\\) to the right of the center \\(C\\), where \\(d < R_1\\), as shown in Figure 1."
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/117828/"
date_modified: "2026-08-04T07:58:57+00:00"
---

# An uncharged, solid, spherical conducting shell has an inner radius \(R_1\) and an outer radius \(R_2\). A small positive point charge \(+Q\) is placed inside the cavity of the shell at a distance \(d\) to the right of the center \(C\), where \(d < R_1\), as shown in Figure 1.

An uncharged, solid, spherical conducting shell has an inner radius \(R_1\) and an outer radius \(R_2\). A small positive point charge \(+Q\) is placed inside the cavity of the shell at a distance \(d\) to the right of the center \(C\), where \(d < R_1\), as shown in Figure 1.

![A cross-sectional view of a spherical shell with an inner circular boundary labeled \(R_1\) and an outer circular boundary labeled \(R_2\). The region between the boundaries is shaded to represent the solid conductor. A horizontal dashed line passes through the center of the shell, which is marked with a dot labeled \(C\). A point charge labeled \(+Q\) is located on the dashed line to the right of \(C\), inside the white inner cavity. A dimension line indicates the distance from \(C\) to \(+Q\) is \(d\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830335-jStT3X.jpg)

**Part a)** **Sketch** a distribution of "+" and "-" signs on Figure 2 to represent the induced charges on the inner and outer surfaces of the conducting shell. Make sure your drawing reflects the relative density of the charges on each surface. *(2 points)*

**Part b)** On Figure 2, **draw** an arrow at each of the four points (\(P_1\), \(P_2\), \(P_3\), and \(P_4\)) to indicate the direction of the electric field vector at that point. If the electric field is exactly zero at a point, **write** "\(E=0\)" next to the point. *(3 points)*

**Part c)** A student claims that the electric field magnitude at \(P_3\) is greater than the electric field magnitude at \(P_4\) because \(P_3\) is closer to the point charge \(+Q\). **Indicate** whether the student's claim is correct or incorrect. - [ ] Correct - [ ] Incorrect **Justify** your answer. *(2 points)*

**Part d)** The point charge \(+Q\) is now moved to the exact center \(C\) of the spherical shell. *(5 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117828/*