---
title: "Four identical point charges, each with charge \\(q\\), are initially positioned infinitely far apart. In Scenario 1, the charges are brought together and held fixed at the four vertices of a regular tetrahedron with edge length \\(a\\). In Scenario 2, the same four charges are brought together and held fixed at the four vertices of a square with side length \\(a\\). What is the ratio of the work required to assemble Scenario 1 to the work required to assemble Scenario 2, \\(W_1 / W_2\\)?"
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url: "https://nerd-notes.com/ubq/118139/"
date_modified: "2026-08-04T08:05:26+00:00"
---

# Four identical point charges, each with charge \(q\), are initially positioned infinitely far apart. In Scenario 1, the charges are brought together and held fixed at the four vertices of a regular tetrahedron with edge length \(a\). In Scenario 2, the same four charges are brought together and held fixed at the four vertices of a square with side length \(a\). What is the ratio of the work required to assemble Scenario 1 to the work required to assemble Scenario 2, \(W_1 / W_2\)?

Four identical point charges, each with charge \(q\), are initially positioned infinitely far apart. In Scenario 1, the charges are brought together and held fixed at the four vertices of a regular tetrahedron with edge length \(a\). In Scenario 2, the same four charges are brought together and held fixed at the four vertices of a square with side length \(a\). What is the ratio of the work required to assemble Scenario 1 to the work required to assemble Scenario 2, \(W_1 / W_2\)?

![Two spatial configurations of point charges labeled Scenario 1 and Scenario 2, placed side by side. On the left, labeled Scenario 1, a regular tetrahedron rendered in thin black outlines with four vertices, each marked by a small filled circle labeled q. All six straight edges of the tetrahedron are equal in length and labeled a. On the right, labeled Scenario 2, a flat square in the plane of the page with four vertices, each marked by a small filled circle labeled q. The four outer sides of the square are labeled a, and two light dashed diagonal lines connect opposite vertices across the interior of the square. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830726-whKz03.jpg)

- **A.** \(\dfrac{8 - 2\sqrt{2}}{7}\)
- **B.** \(\dfrac{4 + \sqrt{2}}{6}\)
- **C.** \(\dfrac{12 - 3\sqrt{2}}{7}\)
- **D.** \(\dfrac{3}{2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118139/*