---
title: "A toroidal solenoid with \\(N\\) tightly wound turns carries a constant current \\(I\\). The toroid has an inner radius \\(a\\) and an outer radius \\(b = 2a\\). What is the ratio \\(B_{\\text{inner}} / B_{\\text{outer}}\\) of the magnetic field magnitude at the inner radius \\(r = a\\) to the magnetic field magnitude at the outer radius \\(r = 2a\\) inside the toroid?"
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url: "https://nerd-notes.com/ubq/118572/"
date_modified: "2026-08-04T08:11:24+00:00"
---

# A toroidal solenoid with \(N\) tightly wound turns carries a constant current \(I\). The toroid has an inner radius \(a\) and an outer radius \(b = 2a\). What is the ratio \(B_{\text{inner}} / B_{\text{outer}}\) of the magnetic field magnitude at the inner radius \(r = a\) to the magnetic field magnitude at the outer radius \(r = 2a\) inside the toroid?

A toroidal solenoid with \(N\) tightly wound turns carries a constant current \(I\). The toroid has an inner radius \(a\) and an outer radius \(b = 2a\). What is the ratio \(B_{\text{inner}} / B_{\text{outer}}\) of the magnetic field magnitude at the inner radius \(r = a\) to the magnetic field magnitude at the outer radius \(r = 2a\) inside the toroid?

![A top-down schematic diagram of a toroidal solenoid centered at the origin. Two concentric dashed circles represent the inner boundary of radius a and the outer boundary of radius b = 2a. A solid black circle represents a circular Amperian loop of radius r between a and b. Uniformly spaced small wire loops are wrapped around the torus. A straight arrow labeled a extends from the center to the inner boundary. A straight arrow labeled b = 2a extends from the center to the outer boundary. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/fig-toroid-1-1785831084-EPDw6Y.jpg)

- **A.** \(1/2\)
- **B.** \(2\)
- **C.** \(4\)
- **D.** \(8\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118572/*