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title: "Two thin, circular, coplanar wire loops share a common center. The inner loop has radius \\(R\\) and carries a counterclockwise current \\(I\\). The outer loop has radius \\(2R\\) and carries a clockwise current \\(I_2\\). Which of the following correctly pairs the required current \\(I_2\\) such that the net magnetic field at the center is zero, with the resulting magnitude of the net magnetic dipole moment \\(\\mu_{\\text{net}}\\)?"
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url: "https://nerd-notes.com/ubq/118545/"
date_modified: "2026-08-04T08:11:16+00:00"
---

# Two thin, circular, coplanar wire loops share a common center. The inner loop has radius \(R\) and carries a counterclockwise current \(I\). The outer loop has radius \(2R\) and carries a clockwise current \(I_2\). Which of the following correctly pairs the required current \(I_2\) such that the net magnetic field at the center is zero, with the resulting magnitude of the net magnetic dipole moment \(\mu_{\text{net}}\)?

Two thin, circular, coplanar wire loops share a common center. The inner loop has radius \(R\) and carries a counterclockwise current \(I\). The outer loop has radius \(2R\) and carries a clockwise current \(I_2\). Which of the following correctly pairs the required current \(I_2\) such that the net magnetic field at the center is zero, with the resulting magnitude of the net magnetic dipole moment \(\mu_{\text{net}}\)?

![Two concentric circular wire loops lying in the plane of the page share a center dot labeled C. The inner circular loop of radius R has a counterclockwise arrow labeled I. The outer circular loop of radius 2R from center C has a clockwise arrow labeled I_2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831076-cIKSDt.jpg)

- **A.** \(I_2 = 2I\) ; \(\mu_{\text{net}} = 7\pi I R^2\)
- **B.** \(I_2 = 2I\) ; \(\mu_{\text{net}} = 3\pi I R^2\)
- **C.** \(I_2 = 4I\) ; \(\mu_{\text{net}} = 15\pi I R^2\)
- **D.** \(I_2 = \dfrac{I}{2}\) ; \(\mu_{\text{net}} = \pi I R^2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118545/*