---
title: "Three point charges are fixed at the vertices of an equilateral triangle with side length \\(a\\), as shown in the figure. Two vertices each hold a charge of \\(+Q\\), while the third vertex holds a charge of \\(-2Q\\). What is the magnitude of the net electric field at the center of the triangle, in terms of \\(Q\\), \\(a\\), and Coulomb’s constant \\(k\\)?"
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url: "https://nerd-notes.com/ubq/117947/"
date_modified: "2026-08-04T08:02:39+00:00"
---

# Three point charges are fixed at the vertices of an equilateral triangle with side length \(a\), as shown in the figure. Two vertices each hold a charge of \(+Q\), while the third vertex holds a charge of \(-2Q\). What is the magnitude of the net electric field at the center of the triangle, in terms of \(Q\), \(a\), and Coulomb’s constant \(k\)?

Three point charges are fixed at the vertices of an equilateral triangle with side length \(a\), as shown in the figure. Two vertices each hold a charge of \(+Q\), while the third vertex holds a charge of \(-2Q\). What is the magnitude of the net electric field at the center of the triangle, in terms of \(Q\), \(a\), and Coulomb's constant \(k\)?

![An equilateral triangle is drawn with a horizontal top side and a bottom vertex pointing downward. The top-left vertex is labeled with +Q. The top-right vertex is labeled with +Q. The bottom vertex is labeled with -2Q. The left side of the triangle has a dimension label a. At the exact geometric center of the triangle, a filled black dot is labeled P. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/triangle-charges-fig-1785830559-6pckJr.jpg)

- **A.** \(\dfrac{3 k Q}{a^2}\)
- **B.** \(\dfrac{9 k Q}{a^2}\)
- **C.** \(\dfrac{12 k Q}{a^2}\)
- **D.** \(\dfrac{18 k Q}{a^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117947/*