---
title: "A rigid planar triangular loop of wire with total resistance \\(R\\) is pulled at a constant velocity into a uniform magnetic field directed perpendicular to the plane of the loop. The apex of the triangle enters the field first at time \\(t = 0\\), and the loop is completely within the field region at time \\(t_1\\). The graph shows the magnitude of the induced electromotive force \\(\\mathcal{E}\\) in the loop as a function of time \\(t\\) during this entry. Which of the following statements correctly interprets a physical quantity associated with the loop?"
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url: "https://nerd-notes.com/ubq/121317/"
date_modified: "2026-08-23T04:59:41+00:00"
---

# A rigid planar triangular loop of wire with total resistance \(R\) is pulled at a constant velocity into a uniform magnetic field directed perpendicular to the plane of the loop. The apex of the triangle enters the field first at time \(t = 0\), and the loop is completely within the field region at time \(t_1\). The graph shows the magnitude of the induced electromotive force \(\mathcal{E}\) in the loop as a function of time \(t\) during this entry. Which of the following statements correctly interprets a physical quantity associated with the loop?

A rigid planar triangular loop of wire with total resistance \(R\) is pulled at a constant velocity into a uniform magnetic field directed perpendicular to the plane of the loop. The apex of the triangle enters the field first at time \(t = 0\), and the loop is completely within the field region at time \(t_1\). The graph shows the magnitude of the induced electromotive force \(\mathcal{E}\) in the loop as a function of time \(t\) during this entry. Which of the following statements correctly interprets a physical quantity associated with the loop?

![A 2D Cartesian coordinate graph showing induced electromotive force versus time. The horizontal axis is labeled t and has a tick mark labeled t_1. The vertical axis is labeled \mathcal{E} and has a tick mark labeled \mathcal{E}_0. The graph contains a single solid line starting at the origin (0,0) and rising linearly with a constant positive slope until it reaches the point (t_1, \mathcal{E}_0). From (t_1, \mathcal{E}_0), a vertical dashed line drops to the horizontal axis at t_1. Bare axes without gridlines. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461181-arzwK1.jpg)

- **A.** The magnetic force opposing the loop's motion increases linearly with time between \(t = 0\) and \(t = t_1\) because the induced EMF increases linearly.
- **B.** The total magnetic flux passing through the loop at \(t = t_1\) is represented by the area under the curve, giving \(\Phi_B = \dfrac{1}{2}\mathcal{E}_0 t_1\).
- **C.** The rate of change of magnetic flux through the loop is constant between \(t = 0\) and \(t = t_1\) because the slope of the \(\mathcal{E}\text{-}t\) graph is constant.
- **D.** The loop would produce an identical \(\mathcal{E}\text{-}t\) graph starting at zero if it were instead pulled into the field base first at the same speed.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121317/*