---
title: "A flat, tightly wound spiral coil lies in a single plane and consists of \\(N\\) turns of fine wire. The spiral has an inner radius \\(a\\) and an outer radius \\(b\\), with the turns distributed uniformly across the radial distance from \\(a\\) to \\(b\\). A steady current \\(I\\) flows through the coil. Which of the following expressions gives the magnitude of the magnetic field at the center of the spiral coil?"
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url: "https://nerd-notes.com/ubq/118556/"
date_modified: "2026-08-04T08:11:21+00:00"
---

# A flat, tightly wound spiral coil lies in a single plane and consists of \(N\) turns of fine wire. The spiral has an inner radius \(a\) and an outer radius \(b\), with the turns distributed uniformly across the radial distance from \(a\) to \(b\). A steady current \(I\) flows through the coil. Which of the following expressions gives the magnitude of the magnetic field at the center of the spiral coil?

A flat, tightly wound spiral coil lies in a single plane and consists of \(N\) turns of fine wire. The spiral has an inner radius \(a\) and an outer radius \(b\), with the turns distributed uniformly across the radial distance from \(a\) to \(b\). A steady current \(I\) flows through the coil. Which of the following expressions gives the magnitude of the magnetic field at the center of the spiral coil?

![A top-down view of a flat spiral coil centered at the origin. The coil consists of tightly wound concentric circular loops filling the region between an inner circular boundary of radius a and an outer circular boundary of radius b. A small arrow along one of the turns indicates a steady current I flowing counterclockwise. The inner radius a is indicated by a dashed radial line from the origin to the inner boundary, labeled a. The outer radius b is indicated by a dashed radial line from the origin to the outer boundary, labeled b. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831081-PLZBHt.jpg)

- **A.** \(\dfrac{\mu_0 N I}{2(b + a)}\)
- **B.** \(\dfrac{\mu_0 N I (b - a)}{2 a b}\)
- **C.** \(\dfrac{\mu_0 N I}{2(b - a)} \ln\left(\dfrac{b}{a}\right)\)
- **D.** \(\dfrac{\mu_0 N I}{b - a} \ln\left(\dfrac{b}{a}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118556/*