---
title: "Four planar, rectangular conducting loops labeled 1, 2, 3, and 4 are pulled to the right at the same constant speed \\(v\\) into a region containing a uniform magnetic field \\(\\vec{B}\\) directed into the page. The dimensions and total resistances of the loops are given in the table.  | Loop | Width perpendicular to \\(\\vec{v}\\) | Length parallel to \\(\\vec{v}\\) | Total resistance | | :— | :— | :— | :— | | 1 | \\(L\\) | \\(L\\) | \\(R_0\\) | | 2 | \\(2L\\) | \\(L\\) | \\(2R_0\\) | | 3 | \\(L\\) | \\(2L\\) | \\(2R_0\\) | | 4 | \\(2L\\) | \\(2L\\) | \\(4R_0\\) |  At an instant when each loop has only its leading edge inside the magnetic field region, which of the following correctly ranks the magnitude of the net magnetic force \\(F\\) exerted on each loop?"
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url: "https://nerd-notes.com/ubq/121311/"
date_modified: "2026-08-23T04:59:40+00:00"
---

# Four planar, rectangular conducting loops labeled 1, 2, 3, and 4 are pulled to the right at the same constant speed \(v\) into a region containing a uniform magnetic field \(\vec{B}\) directed into the page. The dimensions and total resistances of the loops are given in the table.

| Loop | Width perpendicular to \(\vec{v}\) | Length parallel to \(\vec{v}\) | Total resistance |
| :— | :— | :— | :— |
| 1 | \(L\) | \(L\) | \(R_0\) |
| 2 | \(2L\) | \(L\) | \(2R_0\) |
| 3 | \(L\) | \(2L\) | \(2R_0\) |
| 4 | \(2L\) | \(2L\) | \(4R_0\) |

At an instant when each loop has only its leading edge inside the magnetic field region, which of the following correctly ranks the magnitude of the net magnetic force \(F\) exerted on each loop?

Four planar, rectangular conducting loops labeled 1, 2, 3, and 4 are pulled to the right at the same constant speed \(v\) into a region containing a uniform magnetic field \(\vec{B}\) directed into the page. The dimensions and total resistances of the loops are given in the table.

| Loop | Width perpendicular to \(\vec{v}\) | Length parallel to \(\vec{v}\) | Total resistance |
| :--- | :--- | :--- | :--- |
| 1 | \(L\) | \(L\) | \(R_0\) |
| 2 | \(2L\) | \(L\) | \(2R_0\) |
| 3 | \(L\) | \(2L\) | \(2R_0\) |
| 4 | \(2L\) | \(2L\) | \(4R_0\) |

At an instant when each loop has only its leading edge inside the magnetic field region, which of the following correctly ranks the magnitude of the net magnetic force \(F\) exerted on each loop?

![A vertical dashed line divides the drawing into a left region with no field and a right region filled with a rectangular array of six identical x symbols representing a uniform magnetic field \(\vec{B}\) into the page. To the left of the dashed boundary, a rectangular conducting loop of width \(w\) and length \(\ell\) is oriented so its leading edge of length \(w\) is vertical and parallel to the boundary. A single horizontal arrow labeled \(\vec{v}\) extends to the right from the center of the loop's leading edge. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461179-6HZQuD.jpg)

- **A.** \(F_2 > F_4 > F_1 > F_3\)
- **B.** \(F_2 > F_1 = F_4 > F_3\)
- **C.** \(F_4 > F_2 = F_3 > F_1\)
- **D.** \(F_1 = F_2 = F_3 = F_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121311/*