---
title: "A solid insulating sphere of radius \\(R_0\\) contains a total charge \\(Q\\) distributed uniformly throughout its volume. The sphere then expands uniformly to a new radius of \\(2R_0\\) while the total charge \\(Q\\) remains unchanged and uniformly distributed. What is the ratio of the magnitude of the electric field at a distance \\(r = R_0\\) from the center before the expansion to the magnitude of the electric field at that same distance after the expansion, \\(\\dfrac{E_{\\text{initial}}}{E_{\\text{final}}}\\)?"
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/124596/"
date_modified: "2026-09-28T14:08:47+00:00"
---

# A solid insulating sphere of radius \(R_0\) contains a total charge \(Q\) distributed uniformly throughout its volume. The sphere then expands uniformly to a new radius of \(2R_0\) while the total charge \(Q\) remains unchanged and uniformly distributed. What is the ratio of the magnitude of the electric field at a distance \(r = R_0\) from the center before the expansion to the magnitude of the electric field at that same distance after the expansion, \(\dfrac{E_{\text{initial}}}{E_{\text{final}}}\)?

A solid insulating sphere of radius \(R_0\) contains a total charge \(Q\) distributed uniformly throughout its volume. The sphere then expands uniformly to a new radius of \(2R_0\) while the total charge \(Q\) remains unchanged and uniformly distributed. What is the ratio of the magnitude of the electric field at a distance \(r = R_0\) from the center before the expansion to the magnitude of the electric field at that same distance after the expansion, \(\dfrac{E_{\text{initial}}}{E_{\text{final}}}\)?

![Two side-by-side circular diagrams. On the left, labeled Initial, a light-gray shaded circle of radius 2.0 cm is centered on a point. A horizontal solid arrow extends from the center to the right edge of the circle and is labeled \(R_0\). A filled black dot labeled \(P\) lies on the right edge of the circle at distance \(R_0\) from the center. The label \(Q\) is positioned above the circle. On the right, labeled Final, a larger concentric light-gray shaded circle of radius 4.0 cm is centered on a point. A horizontal solid arrow extends from the center to the right edge and is labeled \(2R_0\). A filled black dot labeled \(P\) is located at distance \(R_0\) from the center, positioned inside the shaded circle halfway along the radius. A thin dashed vertical reference line aligns point \(P\) between the two diagrams. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604527-jjpT00.jpg)

- **A.** \(1\)
- **B.** \(4\)
- **C.** \(8\)
- **D.** \(16\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124596/*