---
title: "Three concentric, coplanar circular wire loops—Loop 1, Loop 2, and Loop 3—have radii \\(r\\), \\(2r\\), and \\(3r\\), respectively. The loops are placed in a spatially uniform magnetic field directed perpendicular to the plane of the loops. The magnitude of the magnetic field increases at a constant rate \\(\\dfrac{dB}{dt}\\). All three loops are made from the same wire material with a uniform resistance per unit length. Which of the following correctly ranks the magnitudes of the induced currents \\(I_1\\), \\(I_2\\), and \\(I_3\\) in the loops?"
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/118702/"
date_modified: "2026-08-04T08:13:48+00:00"
---

# Three concentric, coplanar circular wire loops—Loop 1, Loop 2, and Loop 3—have radii \(r\), \(2r\), and \(3r\), respectively. The loops are placed in a spatially uniform magnetic field directed perpendicular to the plane of the loops. The magnitude of the magnetic field increases at a constant rate \(\dfrac{dB}{dt}\). All three loops are made from the same wire material with a uniform resistance per unit length. Which of the following correctly ranks the magnitudes of the induced currents \(I_1\), \(I_2\), and \(I_3\) in the loops?

Three concentric, coplanar circular wire loops—Loop 1, Loop 2, and Loop 3—have radii \(r\), \(2r\), and \(3r\), respectively. The loops are placed in a spatially uniform magnetic field directed perpendicular to the plane of the loops. The magnitude of the magnetic field increases at a constant rate \(\dfrac{dB}{dt}\). All three loops are made from the same wire material with a uniform resistance per unit length. Which of the following correctly ranks the magnitudes of the induced currents \(I_1\), \(I_2\), and \(I_3\) in the loops?

![Three concentric circular loops labeled Loop 1, Loop 2, and Loop 3 lie in the plane of the page. Loop 1 is the innermost circle with radius r. Loop 2 is the middle circle with radius 2r. Loop 3 is the outermost circle with radius 3r. Uniform magnetic field vectors represented by evenly spaced X symbols (directed into the page) cover the entire region containing all three loops. Small dashed lines with arrowheads from the common center indicate the radii r, 2r, and 3r to each loop respectively. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831228-4qZxLA.jpg)

- **A.** \(I_1 > I_2 > I_3\)
- **B.** \(I_3 > I_2 > I_1\)
- **C.** \(I_1 = I_2 = I_3\)
- **D.** \(I_2 > I_3 > I_1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118702/*