---
title: "A flat wire loop of fixed area \\(A\\) is placed in a uniform magnetic field directed perpendicular to the plane of the loop. The magnitude of the magnetic field decreases over time according to \\(B(t) = B_0 \\left(1 – \\dfrac{t}{t_0}\\right)^2\\) for \\(0 \\le t \\le t_0\\), where \\(B_0\\) and \\(t_0\\) are positive constants. Which of the following best describes the graph of the magnitude of the induced electromotive force \\(\\mathcal{E}\\) in the loop as a function of time \\(t\\) for \\(0 \\le t \\le t_0\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/118657/"
date_modified: "2026-08-04T08:13:33+00:00"
---

# A flat wire loop of fixed area \(A\) is placed in a uniform magnetic field directed perpendicular to the plane of the loop. The magnitude of the magnetic field decreases over time according to \(B(t) = B_0 \left(1 – \dfrac{t}{t_0}\right)^2\) for \(0 \le t \le t_0\), where \(B_0\) and \(t_0\) are positive constants. Which of the following best describes the graph of the magnitude of the induced electromotive force \(\mathcal{E}\) in the loop as a function of time \(t\) for \(0 \le t \le t_0\)?

A flat wire loop of fixed area \(A\) is placed in a uniform magnetic field directed perpendicular to the plane of the loop. The magnitude of the magnetic field decreases over time according to \(B(t) = B_0 \left(1 - \dfrac{t}{t_0}\right)^2\) for \(0 \le t \le t_0\), where \(B_0\) and \(t_0\) are positive constants. Which of the following best describes the graph of the magnitude of the induced electromotive force \(\mathcal{E}\) in the loop as a function of time \(t\) for \(0 \le t \le t_0\)?

- **A.** A linearly decreasing function that starts at a maximum positive value at \(t = 0\) and reaches zero at \(t = t_0\)
- **B.** A non-zero constant function from \(t = 0\) to \(t = t_0\)
- **C.** A concave-up quadratic function that decreases from a maximum value at \(t = 0\) to zero at \(t = t_0\)
- **D.** A linearly increasing function that starts at zero at \(t = 0\) and reaches a maximum positive value at \(t = t_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118657/*