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title: "A thin, rigid wire bent into a semicircle of radius \\(R\\) lies in the \\(xy\\)-plane with its endpoints on the \\(x\\)-axis at \\((R, 0)\\) and \\((-R, 0)\\). The wire carries a steady current \\(I\\) directed counterclockwise along the arc for \\(y \\ge 0\\). A uniform magnetic field \\(\\vec{B} = B_0\\,\\hat{k}\\) is directed perpendicular to the \\(xy\\)-plane. In terms of \\(I\\), \\(R\\), and \\(B_0\\), which of the following expressions correctly gives the net magnetic force \\(\\vec{F}\\) exerted on the semicircular wire?"
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url: "https://nerd-notes.com/ubq/121215/"
date_modified: "2026-08-23T04:58:54+00:00"
---

# A thin, rigid wire bent into a semicircle of radius \(R\) lies in the \(xy\)-plane with its endpoints on the \(x\)-axis at \((R, 0)\) and \((-R, 0)\). The wire carries a steady current \(I\) directed counterclockwise along the arc for \(y \ge 0\). A uniform magnetic field \(\vec{B} = B_0\,\hat{k}\) is directed perpendicular to the \(xy\)-plane. In terms of \(I\), \(R\), and \(B_0\), which of the following expressions correctly gives the net magnetic force \(\vec{F}\) exerted on the semicircular wire?

A thin, rigid wire bent into a semicircle of radius \(R\) lies in the \(xy\)-plane with its endpoints on the \(x\)-axis at \((R, 0)\) and \((-R, 0)\). The wire carries a steady current \(I\) directed counterclockwise along the arc for \(y \ge 0\). A uniform magnetic field \(\vec{B} = B_0\,\hat{k}\) is directed perpendicular to the \(xy\)-plane. In terms of \(I\), \(R\), and \(B_0\), which of the following expressions correctly gives the net magnetic force \(\vec{F}\) exerted on the semicircular wire?

![A Cartesian coordinate system shows the horizontal x-axis labeled x and vertical y-axis labeled y intersecting at origin O. A solid black semicircular arc of radius R is centered at the origin, lying entirely in the upper half-plane with endpoints at (R, 0) and (-R, 0) on the x-axis. Two arrowheads on the arc indicate counterclockwise current flow, labeled I. An arrow extends from the origin to the arc at a 45-degree angle labeled R. Five encircled dots indicating a field directed out of the page are arranged in an evenly spaced horizontal line across the region, labeled B. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461134-iqnrEP.jpg)

- **A.** \(\vec{F} = \pi I B_0 R\,\hat{\jmath}\)
- **B.** \(\vec{F} = -2 I B_0 R\,\hat{\jmath}\)
- **C.** \(\vec{F} = I B_0 R\,\hat{\jmath}\)
- **D.** \(\vec{F} = 2 I B_0 R\,\hat{\jmath}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121215/*