---
title: "Three point charges, each with charge \\(+q\\), are initially fixed at the vertices of an equilateral triangle with side length \\(d\\). The net electrostatic force on any one of the charges has magnitude \\(F_i\\). The charge at one vertex is then replaced by a charge of \\(-q\\), while the remaining two charges remain \\(+q\\). What is the ratio \\(F_f / F_i\\) of the new net electrostatic force magnitude \\(F_f\\) on one of the remaining \\(+q\\) charges to its initial magnitude \\(F_i\\), and what is the direction of this new net force?"
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url: "https://nerd-notes.com/ubq/117991/"
date_modified: "2026-08-04T08:02:47+00:00"
---

# Three point charges, each with charge \(+q\), are initially fixed at the vertices of an equilateral triangle with side length \(d\). The net electrostatic force on any one of the charges has magnitude \(F_i\). The charge at one vertex is then replaced by a charge of \(-q\), while the remaining two charges remain \(+q\). What is the ratio \(F_f / F_i\) of the new net electrostatic force magnitude \(F_f\) on one of the remaining \(+q\) charges to its initial magnitude \(F_i\), and what is the direction of this new net force?

Three point charges, each with charge \(+q\), are initially fixed at the vertices of an equilateral triangle with side length \(d\). The net electrostatic force on any one of the charges has magnitude \(F_i\). The charge at one vertex is then replaced by a charge of \(-q\), while the remaining two charges remain \(+q\). What is the ratio \(F_f / F_i\) of the new net electrostatic force magnitude \(F_f\) on one of the remaining \(+q\) charges to its initial magnitude \(F_i\), and what is the direction of this new net force?

![Two side-by-side diagrams labeled Configuration 1 and Configuration 2. Configuration 1 shows an equilateral triangle with vertices labeled 1 at the top, 2 at the bottom-left, and 3 at the bottom-right, each with a circle containing +q. The sides are labeled d. Configuration 2 shows the same equilateral triangle with vertex 1 containing +q, vertex 2 containing +q, and vertex 3 containing -q. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830567-hlYXkC.jpg)

- **A.** Ratio: \(\sqrt{3}\) ; Direction: Parallel to the side connecting the other \(+q\) charge and the \(-q\) charge
- **B.** Ratio: \(\dfrac{1}{	ext{ }\sqrt{3}}\) ; Direction: Parallel to the side connecting the other \(+q\) charge and the \(-q\) charge
- **C.** Ratio: \(\dfrac{1}{	ext{ }\sqrt{3}}\) ; Direction: Perpendicular to the side connecting the other \(+q\) charge and the \(-q\) charge
- **D.** Ratio: \(\dfrac{1}{3}\) ; Direction: Directed away from the center of the triangle

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117991/*