---
title: "Four identical point charges, each of charge $+q$, are held fixed at the four corners of a square with side length $d$ in vacuum. The electric potential is defined to be zero infinitely far from the charges. Which of the following expressions represents the total electric potential energy of this system of four charges?"
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url: "https://nerd-notes.com/ubq/118070/"
date_modified: "2026-08-04T08:04:57+00:00"
---

# Four identical point charges, each of charge $+q$, are held fixed at the four corners of a square with side length $d$ in vacuum. The electric potential is defined to be zero infinitely far from the charges. Which of the following expressions represents the total electric potential energy of this system of four charges?

Four identical point charges, each of charge $+q$, are held fixed at the four corners of a square with side length $d$ in vacuum. The electric potential is defined to be zero infinitely far from the charges. Which of the following expressions represents the total electric potential energy of this system of four charges?

![A square arrangement of four identical point charges. Four small filled circles are located at the four corners of a square of side length d, each labeled +q. Double-headed dimension arrows indicate the length of each horizontal and vertical side as d. No other lines or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830697-b0CDMZ.jpg)

- **A.** \(\dfrac{1}{4\pi\varepsilon_0}\dfrac{q^2}{d}\left(2 + \sqrt{2}\right)\)
- **B.** \(\dfrac{1}{4\pi\varepsilon_0}\dfrac{q^2}{d}\left(4 + \sqrt{2}\right)\)
- **C.** \(\dfrac{1}{4\pi\varepsilon_0}\dfrac{q^2}{d}\left(4 + 2\sqrt{2}\right)\)
- **D.** \(\dfrac{1}{4\pi\varepsilon_0}\dfrac{q^2}{d}\left(6\right)\)

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