---
title: "Four point charges are fixed at the corners of a square of side length \\(2a\\) centered at the origin in the \\(xy\\)-plane, with charges \\(+q\\) at \\((a, a)\\), \\(-q\\) at \\((-a, a)\\), \\(+q\\) at \\((-a, -a)\\), and \\(-q\\) at \\((a, -a)\\).  A small positive test charge \\(+q_0\\) is placed, one at a time, at four designated locations: the center \\(O(0, 0)\\), the edge midpoint \\(A(a, 0)\\), the edge midpoint \\(B(0, a)\\), and the exterior point \\(C(2a, 0)\\).  Which of the following correctly ranks the magnitude of the net electrostatic force \\(F\\) exerted on the test charge at each location?"
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url: "https://nerd-notes.com/ubq/124688/"
date_modified: "2026-09-28T14:09:05+00:00"
---

# Four point charges are fixed at the corners of a square of side length \(2a\) centered at the origin in the \(xy\)-plane, with charges \(+q\) at \((a, a)\), \(-q\) at \((-a, a)\), \(+q\) at \((-a, -a)\), and \(-q\) at \((a, -a)\).

A small positive test charge \(+q_0\) is placed, one at a time, at four designated locations: the center \(O(0, 0)\), the edge midpoint \(A(a, 0)\), the edge midpoint \(B(0, a)\), and the exterior point \(C(2a, 0)\).

Which of the following correctly ranks the magnitude of the net electrostatic force \(F\) exerted on the test charge at each location?

Four point charges are fixed at the corners of a square of side length \(2a\) centered at the origin in the \(xy\)-plane, with charges \(+q\) at \((a, a)\), \(-q\) at \((-a, a)\), \(+q\) at \((-a, -a)\), and \(-q\) at \((a, -a)\).

A small positive test charge \(+q_0\) is placed, one at a time, at four designated locations: the center \(O(0, 0)\), the edge midpoint \(A(a, 0)\), the edge midpoint \(B(0, a)\), and the exterior point \(C(2a, 0)\).

Which of the following correctly ranks the magnitude of the net electrostatic force \(F\) exerted on the test charge at each location?

![A coordinate plane with a horizontal x-axis and vertical y-axis intersecting at an origin labeled O. A square with sides parallel to the axes is centered at the origin, with side length 2a. At each of the four corners sits a small shaded circle representing a point charge: the upper-right corner at (a, a) is labeled +q, the upper-left corner at (-a, a) is labeled -q, the lower-left corner at (-a, -a) is labeled +q, and the lower-right corner at (a, -a) is labeled -q. Four test locations are marked with open circles: point O at the origin (0, 0), point A at the midpoint of the right edge at (a, 0), point B at the midpoint of the top edge at (0, a), and point C along the positive x-axis at (2a, 0). Dashed lines connect the four corner charges to delineate the square perimeter. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604545-sepcsZ.jpg)

- **A.** \(F_O > F_A = F_B > F_C\)
- **B.** \(F_A > F_B > F_C > F_O\)
- **C.** \(F_A = F_B > F_C > F_O\)
- **D.** \(F_A = F_B > F_C = F_O\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124688/*