---
title: "A flat, square loop of wire with side length \\(0.20\\text{ m}\\) is placed in a region containing a uniform electric field. The loop is rotated about an axis that lies in the plane of the loop and is perpendicular to the electric field. The graph shows the electric flux \\(\\Phi_E\\) through the open surface bounded by the loop as a function of the angle \\(\\theta\\) between the electric field and the unit normal vector to the loop. Based on the graph, what is the magnitude of the electric field?"
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url: "https://nerd-notes.com/ubq/124525/"
date_modified: "2026-09-28T14:08:32+00:00"
---

# A flat, square loop of wire with side length \(0.20\text{ m}\) is placed in a region containing a uniform electric field. The loop is rotated about an axis that lies in the plane of the loop and is perpendicular to the electric field. The graph shows the electric flux \(\Phi_E\) through the open surface bounded by the loop as a function of the angle \(\theta\) between the electric field and the unit normal vector to the loop. Based on the graph, what is the magnitude of the electric field?

A flat, square loop of wire with side length \(0.20\text{ m}\) is placed in a region containing a uniform electric field. The loop is rotated about an axis that lies in the plane of the loop and is perpendicular to the electric field. The graph shows the electric flux \(\Phi_E\) through the open surface bounded by the loop as a function of the angle \(\theta\) between the electric field and the unit normal vector to the loop. Based on the graph, what is the magnitude of the electric field?

![A quantitative Cartesian graph with a light gray orthogonal grid. The horizontal axis is labeled \(\theta\text{ (rad)}\) and extends from \(0\) to \(2\pi\), with major tick marks labeled \(0\), \(\pi/2\), \(\pi\), \(3\pi/2\), and \(2\pi\). The vertical axis is labeled \(\Phi_E\text{ (N}\cdot\text{m}^2/\text{C)}\) and extends symmetrically from \(-10.0\) to \(10.0\), with major tick marks and grid lines every \(2.0\text{ units}\) labeled \(-10.0\), \(-8.0\), \(-6.0\), \(-4.0\), \(-2.0\), \(0\), \(2.0\), \(4.0\), \(6.0\), \(8.0\), and \(10.0\). A single solid curve traces a cosine function starting at \((0, 8.0)\), crossing the horizontal axis at \((\pi/2, 0)\), reaching a minimum at \((\pi, -8.0)\), crossing the horizontal axis at \((3\pi/2, 0)\), and ending at a peak of \((2\pi, 8.0)\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604511-fgKqVV.jpg)

- **A.** \(40\text{ N/C}\)
- **B.** \(100\text{ N/C}\)
- **C.** \(200\text{ N/C}\)
- **D.** \(400\text{ N/C}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124525/*