---
title: "A solid conducting sphere of radius \\(R\\) is isolated in empty space. A second system consists of an identical conducting sphere of radius \\(R\\) concentric with an outer thin, hollow conducting spherical shell of radius \\(2R\\). What is the ratio of the capacitance of the two-conductor concentric system to the capacitance of the single isolated sphere, \\(\\dfrac{C_{\\text{concentric}}}{C_{\\text{isolated}}}\\)?"
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url: "https://nerd-notes.com/ubq/124761/"
date_modified: "2026-09-28T14:11:05+00:00"
---

# A solid conducting sphere of radius \(R\) is isolated in empty space. A second system consists of an identical conducting sphere of radius \(R\) concentric with an outer thin, hollow conducting spherical shell of radius \(2R\). What is the ratio of the capacitance of the two-conductor concentric system to the capacitance of the single isolated sphere, \(\dfrac{C_{\text{concentric}}}{C_{\text{isolated}}}\)?

A solid conducting sphere of radius \(R\) is isolated in empty space. A second system consists of an identical conducting sphere of radius \(R\) concentric with an outer thin, hollow conducting spherical shell of radius \(2R\). What is the ratio of the capacitance of the two-conductor concentric system to the capacitance of the single isolated sphere, \(\dfrac{C_{\text{concentric}}}{C_{\text{isolated}}}\)?

![Two diagrams side by side. On the left, labeled System 1, a single solid circle filled with light gray has a dot at its center and an arrow pointing radially outward to its edge labeled R. On the right, labeled System 2, an identical inner solid circle filled with light gray of radius R is shown with an arrow from its center to its perimeter labeled R. Surrounding this inner circle is a larger concentric dashed circle of radius 2R, with an arrow pointing from the common center to the dashed circle labeled 2R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604665-GX6hks.jpg)

- **A.** \(\dfrac{1}{2}\)
- **B.** \(2\)
- **C.** \(4\)
- **D.** \(8\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124761/*