---
title: "A flat, square surface of side length \\(L\\) lies in the \\(xy\\)-plane with vertices at \\((0,0,0)\\), \\((L,0,0)\\), \\((L,L,0)\\), and \\((0,L,0)\\). In Scenario 1, a point charge \\(+q\\) is fixed at position \\((0,0,L)\\), producing an electric flux of magnitude \\(\\Phi_1\\) through the surface. In Scenario 2, the point charge \\(+q\\) is instead fixed at position \\((L/2, L/2, L/2)\\), producing an electric flux of magnitude \\(\\Phi_2\\) through the surface. What is the ratio \\(\\Phi_2 / \\Phi_1\\)?"
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url: "https://nerd-notes.com/ubq/124582/"
date_modified: "2026-09-28T14:08:44+00:00"
---

# A flat, square surface of side length \(L\) lies in the \(xy\)-plane with vertices at \((0,0,0)\), \((L,0,0)\), \((L,L,0)\), and \((0,L,0)\). In Scenario 1, a point charge \(+q\) is fixed at position \((0,0,L)\), producing an electric flux of magnitude \(\Phi_1\) through the surface. In Scenario 2, the point charge \(+q\) is instead fixed at position \((L/2, L/2, L/2)\), producing an electric flux of magnitude \(\Phi_2\) through the surface. What is the ratio \(\Phi_2 / \Phi_1\)?

A flat, square surface of side length \(L\) lies in the \(xy\)-plane with vertices at \((0,0,0)\), \((L,0,0)\), \((L,L,0)\), and \((0,L,0)\). In Scenario 1, a point charge \(+q\) is fixed at position \((0,0,L)\), producing an electric flux of magnitude \(\Phi_1\) through the surface. In Scenario 2, the point charge \(+q\) is instead fixed at position \((L/2, L/2, L/2)\), producing an electric flux of magnitude \(\Phi_2\) through the surface. What is the ratio \(\Phi_2 / \Phi_1\)?

![A three-dimensional Cartesian coordinate system showing axes labeled x, y, and z. In the xy-plane, a square with side length L lies with one vertex at the origin (0,0,0) and opposite diagonal vertex at (L,L,0), shaded light gray. A vertical dashed line extends along the z-axis from the origin to a height L, terminating at a solid black dot labeled Position 1 at (0,0,L). A second vertical dashed line rises from the geometric center of the gray square at (L/2, L/2, 0) to a height of L/2, terminating at a second solid black dot labeled Position 2 at (L/2, L/2, L/2). Thin dashed lines outline a cube of edge length L resting on the square surface to indicate perspective. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604523-ziVWsZ.jpg)

- **A.** \(\dfrac{1}{4}\)
- **B.** \(\dfrac{4}{3}\)
- **C.** \(2\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124582/*