---
title: "Two identical small conducting spheres, each of mass \\(m\\) and carrying charge \\(q\\), are suspended from a common support point by light, nonconducting strings of length \\(L\\). In electrostatic equilibrium, each string makes a small angle \\(\\theta\\) with the vertical (\\(\\theta \\ll 1\\text{ rad}\\)), and the spheres are separated by a horizontal distance \\(d\\). The charge on each sphere is now doubled to \\(2q\\), while the string length \\(L\\) and mass \\(m\\) remain unchanged. What is the ratio of the new electrostatic repulsive force between the spheres to the original electrostatic repulsive force, \\(F_2 / F_1\\)?"
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url: "https://nerd-notes.com/ubq/124757/"
date_modified: "2026-09-28T14:10:30+00:00"
---

# Two identical small conducting spheres, each of mass \(m\) and carrying charge \(q\), are suspended from a common support point by light, nonconducting strings of length \(L\). In electrostatic equilibrium, each string makes a small angle \(\theta\) with the vertical (\(\theta \ll 1\text{ rad}\)), and the spheres are separated by a horizontal distance \(d\). The charge on each sphere is now doubled to \(2q\), while the string length \(L\) and mass \(m\) remain unchanged. What is the ratio of the new electrostatic repulsive force between the spheres to the original electrostatic repulsive force, \(F_2 / F_1\)?

Two identical small conducting spheres, each of mass \(m\) and carrying charge \(q\), are suspended from a common support point by light, nonconducting strings of length \(L\). In electrostatic equilibrium, each string makes a small angle \(\theta\) with the vertical (\(\theta \ll 1\text{ rad}\)), and the spheres are separated by a horizontal distance \(d\). The charge on each sphere is now doubled to \(2q\), while the string length \(L\) and mass \(m\) remain unchanged. What is the ratio of the new electrostatic repulsive force between the spheres to the original electrostatic repulsive force, \(F_2 / F_1\)?

![A horizontal ceiling line at the top with a single pivot point at the center. A vertical dashed line extends downward from the pivot. Two solid straight lines of equal length represent strings suspended from the pivot, symmetrically angled on either side of the vertical dashed line. A curved arc indicates angle \(\theta\) between each string and the central vertical line. The left string is labeled \(L\). At the bottom end of each string is a small solid circle representing a sphere, each labeled with charge \(+q\) and mass \(m\). A horizontal double-headed arrow spans between the centers of the two spheres and is labeled \(d\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604630-s30Bvd.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124757/*