---
title: "Two widely separated conducting spheres, Sphere \\(X\\) of radius \\(3R\\) and Sphere \\(Y\\) of radius \\(R\\), are connected by a long, thin conducting wire. A total positive charge \\(Q\\) is placed on the two-sphere system. After electrostatic equilibrium is established, what is the ratio of the magnitude of the electric field just outside the surface of Sphere \\(X\\) to that just outside the surface of Sphere \\(Y\\), \\(\\dfrac{E_X}{E_Y}\\)?"
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url: "https://nerd-notes.com/ubq/121117/"
date_modified: "2026-08-23T04:58:10+00:00"
---

# Two widely separated conducting spheres, Sphere \(X\) of radius \(3R\) and Sphere \(Y\) of radius \(R\), are connected by a long, thin conducting wire. A total positive charge \(Q\) is placed on the two-sphere system. After electrostatic equilibrium is established, what is the ratio of the magnitude of the electric field just outside the surface of Sphere \(X\) to that just outside the surface of Sphere \(Y\), \(\dfrac{E_X}{E_Y}\)?

Two widely separated conducting spheres, Sphere \(X\) of radius \(3R\) and Sphere \(Y\) of radius \(R\), are connected by a long, thin conducting wire. A total positive charge \(Q\) is placed on the two-sphere system. After electrostatic equilibrium is established, what is the ratio of the magnitude of the electric field just outside the surface of Sphere \(X\) to that just outside the surface of Sphere \(Y\), \(\dfrac{E_X}{E_Y}\)?

![Two solid circles labeled Sphere X and Sphere Y are positioned horizontally apart and connected at their top edges by a single horizontal line representing a thin wire. Sphere X on the left has radius 3R, drawn three times larger than Sphere Y on the right, which has radius R. A radial dashed line extends from the center of Sphere X to its surface, labeled 3R. A radial dashed line extends from the center of Sphere Y to its surface, labeled R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461089-TCGlQL.jpg)

- **A.** \(\dfrac{1}{3}\)
- **B.** \(1\)
- **C.** \(3\)
- **D.** \(9\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121117/*