---
title: "A long coaxial cable consists of a solid inner cylindrical conductor of radius \\(R\\) and a thin outer coaxial cylindrical shell of radius \\(3R\\). The inner conductor carries a uniformly distributed current \\(I\\) directed out of the page, and the outer shell carries an equal current \\(I\\) directed into the page. Four points are located at radial distances \\(r_1 = \\dfrac{R}{2}\\), \\(r_2 = R\\), \\(r_3 = 2R\\), and \\(r_4 = 4R\\) from the central axis of the cable. Which of the following correctly ranks the magnitudes of the magnetic fields \\(B_1\\), \\(B_2\\), \\(B_3\\), and \\(B_4\\) at these four points?"
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url: "https://nerd-notes.com/ubq/121219/"
date_modified: "2026-08-23T04:58:55+00:00"
---

# A long coaxial cable consists of a solid inner cylindrical conductor of radius \(R\) and a thin outer coaxial cylindrical shell of radius \(3R\). The inner conductor carries a uniformly distributed current \(I\) directed out of the page, and the outer shell carries an equal current \(I\) directed into the page. Four points are located at radial distances \(r_1 = \dfrac{R}{2}\), \(r_2 = R\), \(r_3 = 2R\), and \(r_4 = 4R\) from the central axis of the cable. Which of the following correctly ranks the magnitudes of the magnetic fields \(B_1\), \(B_2\), \(B_3\), and \(B_4\) at these four points?

A long coaxial cable consists of a solid inner cylindrical conductor of radius \(R\) and a thin outer coaxial cylindrical shell of radius \(3R\). The inner conductor carries a uniformly distributed current \(I\) directed out of the page, and the outer shell carries an equal current \(I\) directed into the page. Four points are located at radial distances \(r_1 = \dfrac{R}{2}\), \(r_2 = R\), \(r_3 = 2R\), and \(r_4 = 4R\) from the central axis of the cable. Which of the following correctly ranks the magnitudes of the magnetic fields \(B_1\), \(B_2\), \(B_3\), and \(B_4\) at these four points?

![A cross-sectional view of a coaxial cable. A central inner solid circle of radius \(R\) has light-gray shading with four evenly spaced circle-dot symbols indicating current directed out of the page. Concentric with this inner circle is a thin outer circular shell of radius \(3R\) containing four evenly spaced 'x' symbols representing current directed into the page. A horizontal dashed radial line extends from the center origin outward to the right. Along this line, four labeled points are marked with solid black dots: point 1 at radius \(R/2\), point 2 at the outer edge of the inner cylinder at radius \(R\), point 3 in the empty gap at radius \(2R\), and point 4 outside the outer shell at radius \(4R\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461135-LAaUiw.jpg)

- **A.** \(B_2 > B_1 = B_3 > B_4\)
- **B.** \(B_2 > B_3 > B_1 > B_4\)
- **C.** \(B_1 > B_2 > B_3 > B_4\)
- **D.** \(B_2 > B_1 > B_3 > B_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121219/*