---
title: "Two thin, concentric, coplanar circular loops lie in the x y-plane centered at the origin, as shown. The inner loop has radius \\(R\\) and carries a current \\(I\\) in the counterclockwise direction when viewed from the \\(+z\\)-axis. The outer loop has radius \\(2R\\) and carries a current \\(2I\\) in the clockwise direction. Which of the following correctly identifies the net magnetic field vector at the center of the loops (\\(z = 0\\)) and the direction of the net magnetic field along the \\(+z\\)-axis at a distance \\(z \\gg R\\)?"
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url: "https://nerd-notes.com/ubq/118586/"
date_modified: "2026-08-04T08:11:28+00:00"
---

# Two thin, concentric, coplanar circular loops lie in the x y-plane centered at the origin, as shown. The inner loop has radius \(R\) and carries a current \(I\) in the counterclockwise direction when viewed from the \(+z\)-axis. The outer loop has radius \(2R\) and carries a current \(2I\) in the clockwise direction. Which of the following correctly identifies the net magnetic field vector at the center of the loops (\(z = 0\)) and the direction of the net magnetic field along the \(+z\)-axis at a distance \(z \gg R\)?

Two thin, concentric, coplanar circular loops lie in the x y-plane centered at the origin, as shown. The inner loop has radius \(R\) and carries a current \(I\) in the counterclockwise direction when viewed from the \(+z\)-axis. The outer loop has radius \(2R\) and carries a current \(2I\) in the clockwise direction. Which of the following correctly identifies the net magnetic field vector at the center of the loops (\(z = 0\)) and the direction of the net magnetic field along the \(+z\)-axis at a distance \(z \gg R\)?

![Two concentric circular loops lie flat in the xy-plane with their common center at the origin. The inner loop has radius R and features a curved arrow along its perimeter pointing counterclockwise, labeled I. The outer loop has radius 2R and features a curved arrow along its perimeter pointing clockwise, labeled 2I. A horizontal x-axis extends to the right from the center, and a vertical y-axis extends upward from the center. A z-axis extends perpendicular to the plane of the page toward the viewer. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831088-omotEU.jpg)

- **A.** At \(z = 0\): Zero; At \(z \gg R\): \(+z\)-direction
- **B.** At \(z = 0\): Zero; At \(z \gg R\): \(-z\)-direction
- **C.** At \(z = 0\): \(\dfrac{\mu_0 I}{2R}\) in the \(+z\)-direction; At \(z \gg R\): \(+z\)-direction
- **D.** At \(z = 0\): \(\dfrac{\mu_0 I}{2R}\) in the \(-z\)-direction; At \(z \gg R\): \(-z\)-direction

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118586/*