---
title: "A long, flat copper ribbon of width \\(w\\) lies in the \\(xy\\)-plane, centered on the \\(y\\)-axis between \\(x = -w/2\\) and \\(x = w/2\\). The ribbon carries a total current \\(I\\) distributed uniformly across its width in the \\(+y\\)-direction. Which of the following expressions gives the magnitude of the magnetic field \\(B\\) at a point on the \\(z\\)-axis at a distance \\(z\\) above the center of the ribbon?"
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url: "https://nerd-notes.com/ubq/118543/"
date_modified: "2026-08-04T08:11:15+00:00"
---

# A long, flat copper ribbon of width \(w\) lies in the \(xy\)-plane, centered on the \(y\)-axis between \(x = -w/2\) and \(x = w/2\). The ribbon carries a total current \(I\) distributed uniformly across its width in the \(+y\)-direction. Which of the following expressions gives the magnitude of the magnetic field \(B\) at a point on the \(z\)-axis at a distance \(z\) above the center of the ribbon?

A long, flat copper ribbon of width \(w\) lies in the \(xy\)-plane, centered on the \(y\)-axis between \(x = -w/2\) and \(x = w/2\). The ribbon carries a total current \(I\) distributed uniformly across its width in the \(+y\)-direction. Which of the following expressions gives the magnitude of the magnetic field \(B\) at a point on the \(z\)-axis at a distance \(z\) above the center of the ribbon?

![A three-dimensional schematic showing a long, flat copper ribbon lying in the xy-plane, centered along the y-axis, extending from x = -w/2 to x = +w/2. A coordinate system is drawn with an x-axis pointing to the right, a y-axis extending along the length of the ribbon, and a vertical z-axis pointing upward from the center of the ribbon. A total current I flows along the +y direction through the ribbon. An observation point P is located on the z-axis at height z above the origin (0, 0, 0). A thin strip of width dx is highlighted at position x on the ribbon, with a dashed line drawn from the strip to point P, labeled with distance r. An arrow labeled dB points perpendicular to line r at point P in the xz-plane. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831075-j5sIt2.jpg)

- **A.** \(B = \dfrac{\mu_0 I}{2\pi w} \ln\left(1 + \dfrac{w^2}{4z^2}\right)\)
- **B.** \(B = \dfrac{\mu_0 I}{\pi w} \arctan\left(\dfrac{w}{2z}\right)\)
- **C.** \(B = \dfrac{\mu_0 I}{\pi z} \arctan\left(\dfrac{2z}{w}\right)\)
- **D.** \(B = \dfrac{\mu_0 I}{2\pi \sqrt{\left(\dfrac{w}{2}\right)^2 + z^2}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118543/*