---
title: "Four point charges are fixed at the corners of a square with side length \\(d\\), as shown in the diagram. The charges at the top-left, top-right, bottom-right, and bottom-left corners are \\(+2Q\\), \\(-Q\\), \\(-2Q\\), and \\(+Q\\), respectively. A positive test charge \\(+q\\) is placed at the center of the square. Which of the following expressions represents the magnitude of the net electrostatic force acting on the test charge \\(+q\\)?"
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url: "https://nerd-notes.com/ubq/117512/"
date_modified: "2026-08-04T06:52:29+00:00"
---

# Four point charges are fixed at the corners of a square with side length \(d\), as shown in the diagram. The charges at the top-left, top-right, bottom-right, and bottom-left corners are \(+2Q\), \(-Q\), \(-2Q\), and \(+Q\), respectively. A positive test charge \(+q\) is placed at the center of the square. Which of the following expressions represents the magnitude of the net electrostatic force acting on the test charge \(+q\)?

Four point charges are fixed at the corners of a square with side length \(d\), as shown in the diagram. The charges at the top-left, top-right, bottom-right, and bottom-left corners are \(+2Q\), \(-Q\), \(-2Q\), and \(+Q\), respectively. A positive test charge \(+q\) is placed at the center of the square. Which of the following expressions represents the magnitude of the net electrostatic force acting on the test charge \(+q\)?

![A square with side length d is shown in a black outline. At the top-left corner is a small filled circle labeled +2Q. At the top-right corner is a small filled circle labeled -Q. At the bottom-right corner is a small filled circle labeled -2Q. At the bottom-left corner is a small filled circle labeled +Q. Dashed line diagonals connect opposite corners, intersecting at the exact center of the square. At the center intersection point, a small circle with a plus sign is labeled +q. Dimension lines outside the top and left edges of the square indicate side length d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826349-Mfw86m.jpg)

- **A.** \(\dfrac{2\sqrt{2} k Q q}{d^2}\)
- **B.** \(\dfrac{4\sqrt{2} k Q q}{d^2}\)
- **C.** \(\dfrac{2\sqrt{5} k Q q}{d^2}\)
- **D.** \(\dfrac{4\sqrt{5} k Q q}{d^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117512/*