---
title: "Two isolated, solid conducting spheres are located very far apart relative to their radii. Sphere 1 has radius \\(R\\) and carries an initial net charge \\(Q\\), while Sphere 2 has radius \\(3R\\) and is initially uncharged. The spheres are then connected by a long, thin conducting wire and allowed to reach electrostatic equilibrium. Which choice correctly identifies the final net charge \\(Q_{\\text{large}}\\) on Sphere 2 and the ratio of the electric field magnitudes \\(\\dfrac{E_{\\text{small}}}{E_{\\text{large}}}\\) at the outer surface of each sphere?"
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url: "https://nerd-notes.com/ubq/118274/"
date_modified: "2026-08-04T08:08:34+00:00"
---

# Two isolated, solid conducting spheres are located very far apart relative to their radii. Sphere 1 has radius \(R\) and carries an initial net charge \(Q\), while Sphere 2 has radius \(3R\) and is initially uncharged. The spheres are then connected by a long, thin conducting wire and allowed to reach electrostatic equilibrium. Which choice correctly identifies the final net charge \(Q_{\text{large}}\) on Sphere 2 and the ratio of the electric field magnitudes \(\dfrac{E_{\text{small}}}{E_{\text{large}}}\) at the outer surface of each sphere?

Two isolated, solid conducting spheres are located very far apart relative to their radii. Sphere 1 has radius \(R\) and carries an initial net charge \(Q\), while Sphere 2 has radius \(3R\) and is initially uncharged. The spheres are then connected by a long, thin conducting wire and allowed to reach electrostatic equilibrium. Which choice correctly identifies the final net charge \(Q_{\text{large}}\) on Sphere 2 and the ratio of the electric field magnitudes \(\dfrac{E_{\text{small}}}{E_{\text{large}}}\) at the outer surface of each sphere?

![Two isolated conducting spheres drawn side by side, connected by a long thin straight horizontal wire. On the left is a smaller sphere labeled with radius R and charge Q, shown with a thin dashed line from its center to its top edge labeled R. On the right is a larger sphere with radius 3R, drawn three times larger in diameter, labeled with a thin dashed line from its center to its top edge labeled 3R. The thin horizontal line connects the right edge of the small sphere to the left edge of the large sphere. Below the left sphere is text labeled Sphere 1, and below the right sphere is text labeled Sphere 2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830914-f1TpRV.jpg)

- **A.** \(Q_{\text{large}} = \dfrac{1}{4}Q\); \(\dfrac{E_{\text{small}}}{E_{\text{large}}} = 3\)
- **B.** \(Q_{\text{large}} = \dfrac{3}{4}Q\); \(\dfrac{E_{\text{small}}}{E_{\text{large}}} = 3\)
- **C.** \(Q_{\text{large}} = \dfrac{3}{4}Q\); \(\dfrac{E_{\text{small}}}{E_{\text{large}}} = \dfrac{1}{3}\)
- **D.** \(Q_{\text{large}} = \dfrac{1}{2}Q\); \(\dfrac{E_{\text{small}}}{E_{\text{large}}} = 1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118274/*