---
title: "Two spherical conductors, Sphere 1 of radius \\(R\\) and Sphere 2 of radius \\(3R\\), are separated by a distance much greater than their radii. Initially, Sphere 1 carries a net charge of \\(+Q\\) and Sphere 2 carries a net charge of \\(+5Q\\). The spheres are momentarily connected by a thin conducting wire and then disconnected. What is the ratio of the final charge on Sphere 1 to its initial charge, \\(\\dfrac{q_{1,\\text{final}}}{q_{1,\\text{initial}}}\\)?"
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url: "https://nerd-notes.com/ubq/124588/"
date_modified: "2026-09-28T14:08:46+00:00"
---

# Two spherical conductors, Sphere 1 of radius \(R\) and Sphere 2 of radius \(3R\), are separated by a distance much greater than their radii. Initially, Sphere 1 carries a net charge of \(+Q\) and Sphere 2 carries a net charge of \(+5Q\). The spheres are momentarily connected by a thin conducting wire and then disconnected. What is the ratio of the final charge on Sphere 1 to its initial charge, \(\dfrac{q_{1,\text{final}}}{q_{1,\text{initial}}}\)?

Two spherical conductors, Sphere 1 of radius \(R\) and Sphere 2 of radius \(3R\), are separated by a distance much greater than their radii. Initially, Sphere 1 carries a net charge of \(+Q\) and Sphere 2 carries a net charge of \(+5Q\). The spheres are momentarily connected by a thin conducting wire and then disconnected. What is the ratio of the final charge on Sphere 1 to its initial charge, \(\dfrac{q_{1,\text{final}}}{q_{1,\text{initial}}}\)?

![Two circular outlines representing conducting spheres are positioned horizontally on a white background, separated by open space. The left circle, representing Sphere 1, has a smaller radius with a horizontal line segment from its center to its perimeter labeled \(R\), and the text label \(+Q\) positioned directly above the sphere. The right circle, representing Sphere 2, is three times the diameter of the first circle, with a horizontal line segment from its center to its perimeter labeled \(3R\), and the text label \(+5Q\) positioned directly above the sphere. A horizontal dimension line between the bottom centers of the two spheres is labeled \(d \gg R\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604525-wjqbgy.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124588/*