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title: "A flat rectangular loop of wire with length \\(L\\), width \\(w\\), and resistance \\(R\\) moves in the \\(+x\\)-direction at constant speed \\(v_0\\). At time \\(t = 0\\), the front edge of the loop enters a magnetic field region extending from \\(x = 0\\) to \\(x = 2L\\). Within this region, the magnetic field is directed into the page with spatially varying magnitude \\(B(x) = B_0 \\dfrac{x}{L}\\), where \\(B_0\\) is a positive constant, and \\(B = 0\\) elsewhere. Defining counterclockwise current as positive, the induced current \\(I(t)\\) as a function of time increases linearly from \\(0\\) to \\(+I_0\\) for \\(0 \\le t \\le T\\), remains constant at \\(+I_0\\) for \\(T \\le t \\le 2T\\), and jumps to \\(-I_0\\) at \\(t = 2T\\) before rising linearly to \\(0\\) at \\(t = 3T\\), where \\(T = \\dfrac{L}{v_0}\\) and \\(I_0 = \\dfrac{B_0 w v_0}{R}\\). Which of the following claims correctly explains the physical origin of a feature in the \\(I(t)\\) graph?"
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url: "https://nerd-notes.com/ubq/118771/"
date_modified: "2026-08-04T08:14:31+00:00"
---

# A flat rectangular loop of wire with length \(L\), width \(w\), and resistance \(R\) moves in the \(+x\)-direction at constant speed \(v_0\). At time \(t = 0\), the front edge of the loop enters a magnetic field region extending from \(x = 0\) to \(x = 2L\). Within this region, the magnetic field is directed into the page with spatially varying magnitude \(B(x) = B_0 \dfrac{x}{L}\), where \(B_0\) is a positive constant, and \(B = 0\) elsewhere. Defining counterclockwise current as positive, the induced current \(I(t)\) as a function of time increases linearly from \(0\) to \(+I_0\) for \(0 \le t \le T\), remains constant at \(+I_0\) for \(T \le t \le 2T\), and jumps to \(-I_0\) at \(t = 2T\) before rising linearly to \(0\) at \(t = 3T\), where \(T = \dfrac{L}{v_0}\) and \(I_0 = \dfrac{B_0 w v_0}{R}\). Which of the following claims correctly explains the physical origin of a feature in the \(I(t)\) graph?

A flat rectangular loop of wire with length \(L\), width \(w\), and resistance \(R\) moves in the \(+x\)-direction at constant speed \(v_0\). At time \(t = 0\), the front edge of the loop enters a magnetic field region extending from \(x = 0\) to \(x = 2L\). Within this region, the magnetic field is directed into the page with spatially varying magnitude \(B(x) = B_0 \dfrac{x}{L}\), where \(B_0\) is a positive constant, and \(B = 0\) elsewhere. Defining counterclockwise current as positive, the induced current \(I(t)\) as a function of time increases linearly from \(0\) to \(+I_0\) for \(0 \le t \le T\), remains constant at \(+I_0\) for \(T \le t \le 2T\), and jumps to \(-I_0\) at \(t = 2T\) before rising linearly to \(0\) at \(t = 3T\), where \(T = \dfrac{L}{v_0}\) and \(I_0 = \dfrac{B_0 w v_0}{R}\). Which of the following claims correctly explains the physical origin of a feature in the \(I(t)\) graph?

![A line graph plotting induced current I on the vertical axis versus time t on the horizontal axis. The horizontal axis has tick marks labeled 0, T, 2T, and 3T. The vertical axis has tick marks labeled +I_0 at a positive height, 0 at the origin, and -I_0 at an equal negative depth below the horizontal axis. From t = 0 to t = T, a solid straight line segment rises linearly from (0, 0) to (T, +I_0). From t = T to t = 2T, a solid horizontal line segment connects (T, +I_0) to (2T, +I_0). At t = 2T, a vertical dashed line connects (2T, +I_0) down to (2T, -I_0). From t = 2T to t = 3T, a solid straight line segment rises linearly from (2T, -I_0) to (3T, 0). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831270-BIsl2T.jpg)

- **A.** The current is constant during \(T < t < 2T\) because no magnetic flux enters or leaves the loop while it is entirely contained inside the field region.
- **B.** The linear increase in current during \(0 < t < T\) is caused solely by the constant rate at which the area of the loop inside the field region increases.
- **C.** The current flips sign to \(-I_0\) at \(t = 2T\) because the direction of the magnetic field vector reverses as the loop begins exiting the region.
- **D.** The constant positive current \(+I_0\) during \(T < t < 2T\) arises because the difference in magnetic field strength between the front and rear edges of the loop remains constant as it moves through the region.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118771/*