---
title: "A solid insulating sphere of radius \\(R\\) carries a net charge \\(+Q\\) distributed uniformly throughout its volume. A separate point charge \\(+Q\\) is isolated in space. Let \\(\\Delta V_{\\text{sphere}}\\) be the magnitude of the electric potential difference between radial distances \\(r = R\\) and \\(r = 2R\\) from the center of the sphere, and let \\(\\Delta V_{\\text{point}}\\) be the magnitude of the electric potential difference between distances \\(r = R\\) and \\(r = 2R\\) from the point charge. What is the ratio \\(\\dfrac{\\Delta V_{\\text{sphere}}}{\\Delta V_{\\text{point}}}\\)?"
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url: "https://nerd-notes.com/ubq/118106/"
date_modified: "2026-08-04T08:05:09+00:00"
---

# A solid insulating sphere of radius \(R\) carries a net charge \(+Q\) distributed uniformly throughout its volume. A separate point charge \(+Q\) is isolated in space. Let \(\Delta V_{\text{sphere}}\) be the magnitude of the electric potential difference between radial distances \(r = R\) and \(r = 2R\) from the center of the sphere, and let \(\Delta V_{\text{point}}\) be the magnitude of the electric potential difference between distances \(r = R\) and \(r = 2R\) from the point charge. What is the ratio \(\dfrac{\Delta V_{\text{sphere}}}{\Delta V_{\text{point}}}\)?

A solid insulating sphere of radius \(R\) carries a net charge \(+Q\) distributed uniformly throughout its volume. A separate point charge \(+Q\) is isolated in space. Let \(\Delta V_{\text{sphere}}\) be the magnitude of the electric potential difference between radial distances \(r = R\) and \(r = 2R\) from the center of the sphere, and let \(\Delta V_{\text{point}}\) be the magnitude of the electric potential difference between distances \(r = R\) and \(r = 2R\) from the point charge. What is the ratio \(\dfrac{\Delta V_{\text{sphere}}}{\Delta V_{\text{point}}}\)?

![Two side-by-side scenarios labeled Scenario 1 and Scenario 2. On the left, Scenario 1 shows a shaded circle of radius R centered at the origin, labeled +Q. Dashed concentric circular paths of radii R and 2R encircle the center. A horizontal dashed line extends from the center outward to the right, with tick marks labeled r = R and r = 2R. On the right, Scenario 2 shows a small solid dot representing a point charge, labeled +Q. Dashed concentric circular paths of radii R and 2R surround the point charge, with a horizontal dashed line extending to the right with tick marks labeled r = R and r = 2R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830709-bwZsII.jpg)

- **A.** \(\dfrac{1}{4}\)
- **B.** \(\dfrac{1}{2}\)
- **C.** \(\dfrac{3}{4}\)
- **D.** \(1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118106/*