---
title: "A long ideal solenoid of radius \\(R\\) carries a constant current, producing a uniform magnetic field \\(B\\) directed along its central axis inside the solenoid, while the magnetic field outside the solenoid is negligible. Three flat, circular, concentric wire loops—Loop 1 with radius \\(r_1 = 0.5R\\), Loop 2 with radius \\(r_2 = 1.5R\\), and Loop 3 with radius \\(r_3 = 2.5R\\)—are placed in a plane perpendicular to the central axis of the solenoid. Which of the following correctly ranks the magnetic fluxes \\(\\Phi_1\\), \\(\\Phi_2\\), and \\(\\Phi_3\\) through Loop 1, Loop 2, and Loop 3, respectively?"
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url: "https://nerd-notes.com/ubq/118687/"
date_modified: "2026-08-04T08:13:46+00:00"
---

# A long ideal solenoid of radius \(R\) carries a constant current, producing a uniform magnetic field \(B\) directed along its central axis inside the solenoid, while the magnetic field outside the solenoid is negligible. Three flat, circular, concentric wire loops—Loop 1 with radius \(r_1 = 0.5R\), Loop 2 with radius \(r_2 = 1.5R\), and Loop 3 with radius \(r_3 = 2.5R\)—are placed in a plane perpendicular to the central axis of the solenoid. Which of the following correctly ranks the magnetic fluxes \(\Phi_1\), \(\Phi_2\), and \(\Phi_3\) through Loop 1, Loop 2, and Loop 3, respectively?

A long ideal solenoid of radius \(R\) carries a constant current, producing a uniform magnetic field \(B\) directed along its central axis inside the solenoid, while the magnetic field outside the solenoid is negligible. Three flat, circular, concentric wire loops—Loop 1 with radius \(r_1 = 0.5R\), Loop 2 with radius \(r_2 = 1.5R\), and Loop 3 with radius \(r_3 = 2.5R\)—are placed in a plane perpendicular to the central axis of the solenoid. Which of the following correctly ranks the magnetic fluxes \(\Phi_1\), \(\Phi_2\), and \(\Phi_3\) through Loop 1, Loop 2, and Loop 3, respectively?

![A cross-sectional diagram showing a circular solenoid of radius \(R\), shaded light blue to indicate a uniform magnetic field directed into the page. Three concentric circular wire loops are drawn centered on the solenoid: Loop 1 with radius \(0.5R\) lies entirely inside the blue shaded circle; Loop 2 with radius \(1.5R\) lies outside the blue circle; Loop 3 with radius \(2.5R\) lies furthest outward. Arrowed dimension lines indicate radii \(R\), \(0.5R\), \(1.5R\), and \(2.5R\) extending from the shared central origin toward the upper-right. No other labels, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831226-Tfqn4d.jpg)

- **A.** \(\Phi_2 = \Phi_3 > \Phi_1\)
- **B.** \(\Phi_3 > \Phi_2 > \Phi_1\)
- **C.** \(\Phi_1 = \Phi_2 = \Phi_3\)
- **D.** \(\Phi_1 > \Phi_2 = \Phi_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118687/*