---
title: "Two concentric, circular wire loops of radius \\(R\\) and \\(2R\\) lie in the same plane. A uniform magnetic field \\(\\vec{B}\\) is directed perpendicular to the plane of the loops. What is the ratio \\(\\dfrac{\\Phi_1}{\\Phi_2}\\) of the magnetic flux through the inner loop of radius \\(R\\) to the magnetic flux through the outer loop of radius \\(2R\\)?"
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url: "https://nerd-notes.com/ubq/121335/"
date_modified: "2026-08-23T04:59:46+00:00"
---

# Two concentric, circular wire loops of radius \(R\) and \(2R\) lie in the same plane. A uniform magnetic field \(\vec{B}\) is directed perpendicular to the plane of the loops. What is the ratio \(\dfrac{\Phi_1}{\Phi_2}\) of the magnetic flux through the inner loop of radius \(R\) to the magnetic flux through the outer loop of radius \(2R\)?

Two concentric, circular wire loops of radius \(R\) and \(2R\) lie in the same plane. A uniform magnetic field \(\vec{B}\) is directed perpendicular to the plane of the loops. What is the ratio \(\dfrac{\Phi_1}{\Phi_2}\) of the magnetic flux through the inner loop of radius \(R\) to the magnetic flux through the outer loop of radius \(2R\)?

![Two concentric circles in the plane of the page, centered at the same point. The smaller inner circle is labeled with a radius arrow from the center pointing up and to the right at 45 degrees, labeled R. The larger outer circle has a radius arrow extending from the center down and to the right at 45 degrees, labeled 2R. A uniform grid of six magnetic field symbols, each depicted as an x indicating a field directed into the page, is distributed evenly around the circles. A single label B with an arrow is placed near the top right of the field region. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461186-fklcbS.jpg)

- **A.** \(\dfrac{1}{4}\)
- **B.** \(\dfrac{1}{2}\)
- **C.** \(2\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121335/*