---
title: "A thin circular wire loop of radius \\(R\\) lies in the \\(xy\\)-plane and carries a steady current \\(I\\). The magnitude of the magnetic field along the central \\(z\\)-axis perpendicular to the loop is given by \\(B(z) = \\dfrac{\\mu_0 I R^2}{2(R^2 + z^2)^{3/2}}\\), where \\(z\\) is the distance from the center of the loop. Which of the following expressions represents the approximate magnitude of the magnetic field at a point on the axis very far from the loop (\\(z \\gg R\\))?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/118487/"
date_modified: "2026-08-04T08:11:03+00:00"
---

# A thin circular wire loop of radius \(R\) lies in the \(xy\)-plane and carries a steady current \(I\). The magnitude of the magnetic field along the central \(z\)-axis perpendicular to the loop is given by \(B(z) = \dfrac{\mu_0 I R^2}{2(R^2 + z^2)^{3/2}}\), where \(z\) is the distance from the center of the loop. Which of the following expressions represents the approximate magnitude of the magnetic field at a point on the axis very far from the loop (\(z \gg R\))?

A thin circular wire loop of radius \(R\) lies in the \(xy\)-plane and carries a steady current \(I\). The magnitude of the magnetic field along the central \(z\)-axis perpendicular to the loop is given by \(B(z) = \dfrac{\mu_0 I R^2}{2(R^2 + z^2)^{3/2}}\), where \(z\) is the distance from the center of the loop. Which of the following expressions represents the approximate magnitude of the magnetic field at a point on the axis very far from the loop (\(z \gg R\))?

![A circular loop of wire with radius R is shown in perspective as a flat ellipse centered at the origin. A vertical z-axis passes perpendicular to the plane of the loop through its center. An arrow labeled I along the circular loop indicates counterclockwise current as viewed from above the plane. The center of the loop is marked with a point. A vertical dashed line extends along the positive z-axis from the center of the loop to a point P located at a distance z above the center. A solid arrow labeled R extends from the center of the loop horizontally to the outer edge of the loop. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831062-Rfnjwp.jpg)

- **A.** \(\dfrac{\mu_0 I}{2 z}\)
- **B.** \(\dfrac{\mu_0 I R}{2 z^2}\)
- **C.** \(\dfrac{\mu_0 I R^3}{2 z^4}\)
- **D.** \(\dfrac{\mu_0 I R^2}{2 z^3}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118487/*