---
title: "A single circular wire loop of radius \\(R\\) lies in the \\(xy\\)-plane, centered at the origin, and carries a steady current \\(I\\). A student applies the Biot-Savart law to analyze the magnetic field magnitude \\(B\\) at points along the central \\(z\\)-axis. Which of the following correctly describes the qualitative features of the graph of \\(B\\) as a function of \\(z\\) over the domain \\(-\\infty < z < \\infty\\)?"
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url: "https://nerd-notes.com/ubq/121231/"
date_modified: "2026-08-23T04:58:57+00:00"
---

# A single circular wire loop of radius \(R\) lies in the \(xy\)-plane, centered at the origin, and carries a steady current \(I\). A student applies the Biot-Savart law to analyze the magnetic field magnitude \(B\) at points along the central \(z\)-axis. Which of the following correctly describes the qualitative features of the graph of \(B\) as a function of \(z\) over the domain \(-\infty < z < \infty\)?

A single circular wire loop of radius \(R\) lies in the \(xy\)-plane, centered at the origin, and carries a steady current \(I\). A student applies the Biot-Savart law to analyze the magnetic field magnitude \(B\) at points along the central \(z\)-axis. Which of the following correctly describes the qualitative features of the graph of \(B\) as a function of \(z\) over the domain \(-\infty < z < \infty\)?

![A circular wire loop of radius \(R\) drawn as a flat horizontal ellipse in perspective, centered at the origin. A vertical dashed line passes through the center of the loop, oriented along the vertical direction and labeled \(z\). An arrow along the loop indicates a steady current \(I\). A point on the positive \(z\)-axis is marked at a distance \(z\) above the loop center. An arrow labeled \(R\) extends horizontally from the origin to the loop edge. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461137-5MUb2t.jpg)

- **A.** A symmetric curve with a sharp peak at \(z = 0\) having non-zero slope, which decays asymptotically proportional to \(\dfrac{1}{|z|}\) as \(|z| \to \infty\)
- **B.** A symmetric curve with a vertical asymptote at \(z = 0\) where \(B \to \infty\), which decays asymptotically proportional to \(\dfrac{1}{z^2}\) as \(|z| \to \infty\)
- **C.** A smooth symmetric curve with a single local maximum and zero slope at \(z = 0\), which decays asymptotically proportional to \(\dfrac{1}{|z|^3}\) as \(|z| \to \infty\)
- **D.** A symmetric curve that is zero at \(z = 0\), reaches local maxima at non-zero values of \(|z|\), and decays asymptotically to zero as \(|z| \to \infty\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121231/*