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title: "A rigid planar triangular conducting loop of resistance \\(R\\) enters a region of uniform magnetic field perpendicular to the loop at a constant velocity \\(v\\), entering vertex-first at time \\(t = 0\\). The loop becomes completely immersed in the field at time \\(t_1\\) and remains entirely within the field until after time \\(t_2\\). The graph shows the magnetic flux \\(\\Phi_B\\) through the loop as a function of time \\(t\\). Which of the following statements correctly relates the features of the graph to the electrical or mechanical behavior of the loop?"
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url: "https://nerd-notes.com/ubq/125024/"
date_modified: "2026-09-28T14:13:19+00:00"
---

# A rigid planar triangular conducting loop of resistance \(R\) enters a region of uniform magnetic field perpendicular to the loop at a constant velocity \(v\), entering vertex-first at time \(t = 0\). The loop becomes completely immersed in the field at time \(t_1\) and remains entirely within the field until after time \(t_2\). The graph shows the magnetic flux \(\Phi_B\) through the loop as a function of time \(t\). Which of the following statements correctly relates the features of the graph to the electrical or mechanical behavior of the loop?

A rigid planar triangular conducting loop of resistance \(R\) enters a region of uniform magnetic field perpendicular to the loop at a constant velocity \(v\), entering vertex-first at time \(t = 0\). The loop becomes completely immersed in the field at time \(t_1\) and remains entirely within the field until after time \(t_2\). The graph shows the magnetic flux \(\Phi_B\) through the loop as a function of time \(t\). Which of the following statements correctly relates the features of the graph to the electrical or mechanical behavior of the loop?

![A 2D Cartesian graph with bare axes and no gridlines. The horizontal axis is labeled t at its right end, and the vertical axis is labeled \Phi_B at its top end. The origin is marked 0. A single solid black curve begins at the origin with zero initial slope and curves smoothly upward with concave-upward curvature until reaching a point with coordinates marked by dashed guide lines extending to \Phi_{\text{max}} on the vertical axis and t_1 on the horizontal axis. From t_1 to t_2, the solid black curve continues horizontally at the constant value \Phi_{\text{max}}. A vertical dashed guide line drops from the curve at t_2 to a tick mark labeled t_2 on the horizontal axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604799-U06M8Z.jpg)

- **A.** The rate of thermal energy dissipation in the loop reaches its maximum just prior to \(t = t_1\) because the power is proportional to the square of the slope of the \(\Phi_B\) versus \(t\) graph, which is greatest at that instant.
- **B.** The induced current in the loop is greatest during the interval \(t_1 < t < t_2\) because the magnetic flux through the loop attains its maximum value.
- **C.** The rate of thermal energy dissipation in the loop increases linearly with time during the interval \(0 < t < t_1\) because the slope of the \(\Phi_B\) versus \(t\) graph increases at a constant rate.
- **D.** The external force required to maintain the constant velocity is constant during the interval \(0 < t < t_1\) because the curvature (second derivative \(\dfrac{d^2\Phi_B}{dt^2}\)) of the graph is constant.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125024/*