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title: "A thin wire carrying a steady current \\(I\\) lies in the \\(xy\\)-plane and consists of three connected sections: a semi-infinite straight section extending along the negative \\(x\\)-axis from \\(x = -\\infty\\) to \\(x = -R\\), a quarter-circular arc of radius \\(R\\) centered at the origin connecting \\((-R, 0)\\) to \\((0, R)\\), and a semi-infinite straight section extending along the positive \\(y\\)-axis from \\(y = R\\) to \\(y = +\\infty\\). Current \\(I\\) flows continuously through the sections in that order. Which of the following correctly describes the magnitude and direction of the net magnetic field \\(\\vec{B}\\) at the origin?"
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url: "https://nerd-notes.com/ubq/124992/"
date_modified: "2026-09-28T14:12:48+00:00"
---

# A thin wire carrying a steady current \(I\) lies in the \(xy\)-plane and consists of three connected sections: a semi-infinite straight section extending along the negative \(x\)-axis from \(x = -\infty\) to \(x = -R\), a quarter-circular arc of radius \(R\) centered at the origin connecting \((-R, 0)\) to \((0, R)\), and a semi-infinite straight section extending along the positive \(y\)-axis from \(y = R\) to \(y = +\infty\). Current \(I\) flows continuously through the sections in that order. Which of the following correctly describes the magnitude and direction of the net magnetic field \(\vec{B}\) at the origin?

A thin wire carrying a steady current \(I\) lies in the \(xy\)-plane and consists of three connected sections: a semi-infinite straight section extending along the negative \(x\)-axis from \(x = -\infty\) to \(x = -R\), a quarter-circular arc of radius \(R\) centered at the origin connecting \((-R, 0)\) to \((0, R)\), and a semi-infinite straight section extending along the positive \(y\)-axis from \(y = R\) to \(y = +\infty\). Current \(I\) flows continuously through the sections in that order. Which of the following correctly describes the magnitude and direction of the net magnetic field \(\vec{B}\) at the origin?

![A Cartesian coordinate plane with horizontal axis labeled x and vertical axis labeled y, intersecting at origin O. A thick solid line represents a wire carrying current I. The wire begins on the negative x-axis with an open end at the far left, extends along the horizontal axis to point (-R, 0), curves smoothly upward as a quarter-circle arc of radius R centered at O through the second quadrant to point (0, R) on the positive y-axis, and continues vertically upward along the positive y-axis with an open end at the top. Three small arrowheads along the wire indicate current direction: one pointing rightward along the negative x-axis, one pointing along the curved arc toward the positive y-axis, and one pointing upward along the positive y-axis. A label I is positioned adjacent to the wire. A radial dashed line segment connects origin O to the curved arc, labeled R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604768-iCZuco.jpg)

- **A.** Magnitude \(\dfrac{\mu_0 I}{R}\left(\dfrac{1}{2\pi} + \dfrac{1}{8}\right)\), directed into the page
- **B.** Magnitude \(\dfrac{\mu_0 I}{R}\left(\dfrac{1}{2\pi} + \dfrac{1}{8}\right)\), directed out of the page
- **C.** Magnitude \(\dfrac{\mu_0 I}{8R}\), directed out of the page
- **D.** Magnitude \(\dfrac{\mu_0 I}{8R}\), directed into the page

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124992/*