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title: "A rigid rectangular coil of mass m, width w, and N turns is suspended vertically from an ideal spring of force constant k. The bottom horizontal segment of the coil hangs in a uniform horizontal magnetic field B directed perpendicular to the plane of the coil, while the top segment remains outside the field. When a current I is established in the coil, the resulting downward magnetic force causes an additional vertical equilibrium displacement \\(\\Delta y\\) from the coil’s initial unpowered position. If a linear graph of \\(\\Delta y\\) on the vertical axis versus I on the horizontal axis yields a line of best fit with slope S, which of the following correctly identifies what S represents and the resulting expression for B?"
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url: "https://nerd-notes.com/ubq/124887/"
date_modified: "2026-09-28T14:11:49+00:00"
---

# A rigid rectangular coil of mass m, width w, and N turns is suspended vertically from an ideal spring of force constant k. The bottom horizontal segment of the coil hangs in a uniform horizontal magnetic field B directed perpendicular to the plane of the coil, while the top segment remains outside the field. When a current I is established in the coil, the resulting downward magnetic force causes an additional vertical equilibrium displacement \(\Delta y\) from the coil’s initial unpowered position. If a linear graph of \(\Delta y\) on the vertical axis versus I on the horizontal axis yields a line of best fit with slope S, which of the following correctly identifies what S represents and the resulting expression for B?

A rigid rectangular coil of mass m, width w, and N turns is suspended vertically from an ideal spring of force constant k. The bottom horizontal segment of the coil hangs in a uniform horizontal magnetic field B directed perpendicular to the plane of the coil, while the top segment remains outside the field. When a current I is established in the coil, the resulting downward magnetic force causes an additional vertical equilibrium displacement \(\Delta y\) from the coil's initial unpowered position. If a linear graph of \(\Delta y\) on the vertical axis versus I on the horizontal axis yields a line of best fit with slope S, which of the following correctly identifies what S represents and the resulting expression for B?

![A horizontal ceiling support is shown at the top. Suspended vertically from the center of the ceiling is a helical spring with label k. Attached to the bottom end of the spring is a rigid, vertical rectangular coil of width w. The coil consists of two vertical parallel sides and two horizontal parallel sides. A small arrow along the wire indicates current I. The upper horizontal segment of the coil hangs in empty space. The lower horizontal segment of width w hangs inside a bounded rectangular region indicated by a dashed outline. Inside this rectangular region, an array of six evenly spaced \times symbols arranged in two horizontal rows of three indicates a uniform magnetic field labeled \vec{B}. A vertical dashed reference line beside the coil shows a downward arrow labeled \Delta y indicating displacement from an initial horizontal tick mark. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604709-HakbCO.jpg)

- **A.** Slope \(S = \dfrac{k B}{N w}\), yielding \(B = \dfrac{N w S}{k}\)
- **B.** Slope \(S = \dfrac{N w B}{k}\), yielding \(B = \dfrac{k S}{N w}\)
- **C.** Slope \(S = \dfrac{k}{N w B}\), yielding \(B = \dfrac{k}{N w S}\)
- **D.** Slope \(S = \dfrac{N w B}{m g}\), yielding \(B = \dfrac{m g S}{N w}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124887/*