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title: "A rigid square loop of side length \\(L\\) lies flat in the \\(xy\\)-plane and carries a steady counterclockwise current \\(I\\). A uniform magnetic field \\(\\vec{B} = B_0 \\hat{i}\\) points in the positive \\(x\\)-direction across the plane of the loop. Axis 1 lies along the line \\(x = 0\\) (passing through the center of the loop), and Axis 2 lies along the line \\(x = -\\dfrac{L}{2}\\) (passing through the left edge of the loop), with both axes parallel to the \\(y\\)-axis. Which of the following correctly compares the magnitudes of the net magnetic torque about Axis 1 (\\(\\tau_1\\)) and Axis 2 (\\(\\tau_2\\)), and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/118551/"
date_modified: "2026-08-04T08:11:20+00:00"
---

# A rigid square loop of side length \(L\) lies flat in the \(xy\)-plane and carries a steady counterclockwise current \(I\). A uniform magnetic field \(\vec{B} = B_0 \hat{i}\) points in the positive \(x\)-direction across the plane of the loop. Axis 1 lies along the line \(x = 0\) (passing through the center of the loop), and Axis 2 lies along the line \(x = -\dfrac{L}{2}\) (passing through the left edge of the loop), with both axes parallel to the \(y\)-axis. Which of the following correctly compares the magnitudes of the net magnetic torque about Axis 1 (\(\tau_1\)) and Axis 2 (\(\tau_2\)), and provides the correct physical justification?

A rigid square loop of side length \(L\) lies flat in the \(xy\)-plane and carries a steady counterclockwise current \(I\). A uniform magnetic field \(\vec{B} = B_0 \hat{i}\) points in the positive \(x\)-direction across the plane of the loop. Axis 1 lies along the line \(x = 0\) (passing through the center of the loop), and Axis 2 lies along the line \(x = -\dfrac{L}{2}\) (passing through the left edge of the loop), with both axes parallel to the \(y\)-axis. Which of the following correctly compares the magnitudes of the net magnetic torque about Axis 1 (\(\tau_1\)) and Axis 2 (\(\tau_2\)), and provides the correct physical justification?

![A square loop of side length L lies flat in the xy-plane, centered at the origin. Current I flows counterclockwise around the perimeter: top segment carries current leftward (-x), left segment carries current downward (-y), bottom segment carries current rightward (+x), and right segment carries current upward (+y). Three horizontal, parallel arrows labeled B_0 point to the right (+x direction) across the loop. Axis 1 is drawn as a vertical dashed line along the y-axis at x = 0 and is labeled 'Axis 1'. Axis 2 is drawn as a vertical dashed line along the left edge at x = -L/2 and is labeled 'Axis 2'. No other labels or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831079-H75O0M.jpg)

- **A.** \(\tau_1 < \tau_2\) because the moment arm from Axis 2 to the rightmost segment is twice as long as the moment arm from Axis 1 to either vertical segment.
- **B.** \(\tau_1 > \tau_2\) because magnetic forces act on two segments relative to Axis 1, whereas only one segment produces torque relative to Axis 2.
- **C.** \(\tau_1 = 0\) and \(\tau_2 > 0\) because equal and opposite magnetic forces acting symmetrically about the central axis cancel out all rotational effects.
- **D.** \(\tau_1 = \tau_2\) because the net magnetic force on the loop is zero, making the net torque independent of the location of the parallel axis of rotation.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118551/*