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title: "A long coaxial cable consists of a solid cylindrical inner conductor of radius \\(a = 2.0 \\text{ mm}\\) and a concentric cylindrical outer conductor of inner radius \\(b = 4.0 \\text{ mm}\\) and outer radius \\(c = 8.0 \\text{ mm}\\). The inner conductor carries current directed out of the page with a non-uniform volume current density \\(J(r) = C r\\), where \\(C = 6.0 \\times 10^7 \\text{ A/m}^3\\) and \\(r\\) is the radial distance from the central axis. The outer conductor carries a uniformly distributed total current of \\(2.5 \\text{ A}\\) directed into the page. What is the magnitude of the magnetic field at the inner boundary of the outer conductor (\\(r = 4.0 \\text{ mm}\\))?"
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url: "https://nerd-notes.com/ubq/124879/"
date_modified: "2026-09-28T14:11:47+00:00"
---

# A long coaxial cable consists of a solid cylindrical inner conductor of radius \(a = 2.0 \text{ mm}\) and a concentric cylindrical outer conductor of inner radius \(b = 4.0 \text{ mm}\) and outer radius \(c = 8.0 \text{ mm}\). The inner conductor carries current directed out of the page with a non-uniform volume current density \(J(r) = C r\), where \(C = 6.0 \times 10^7 \text{ A/m}^3\) and \(r\) is the radial distance from the central axis. The outer conductor carries a uniformly distributed total current of \(2.5 \text{ A}\) directed into the page. What is the magnitude of the magnetic field at the inner boundary of the outer conductor (\(r = 4.0 \text{ mm}\))?

A long coaxial cable consists of a solid cylindrical inner conductor of radius \(a = 2.0 \text{ mm}\) and a concentric cylindrical outer conductor of inner radius \(b = 4.0 \text{ mm}\) and outer radius \(c = 8.0 \text{ mm}\). The inner conductor carries current directed out of the page with a non-uniform volume current density \(J(r) = C r\), where \(C = 6.0 \times 10^7 \text{ A/m}^3\) and \(r\) is the radial distance from the central axis. The outer conductor carries a uniformly distributed total current of \(2.5 \text{ A}\) directed into the page. What is the magnitude of the magnetic field at the inner boundary of the outer conductor (\(r = 4.0 \text{ mm}\))?

![A grayscale cross-sectional view of a coaxial cable perpendicular to its central axis. At the center is a solid circle of radius \(a\) filled with light gray shading, marked with a central black dot and an arrow pointing toward the upper-right at 45 degrees labeled \(a\). Surrounding this inner circle is a white annular region extending to a circular boundary of radius \(b\), with an arrow from the center toward the upper-right at 30 degrees labeled \(b\). Outside this boundary is an outer concentric annular ring of inner radius \(b\) and outer radius \(c\), filled with diagonal hatch lines, with an arrow from the center toward the upper-right at 15 degrees labeled \(c\). A dot symbol labeled \(J(r)\) sits inside the inner shaded cylinder, and an 'X' symbol labeled \(I\) sits inside the outer hatched ring. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604707-u3fA07.jpg)

- **A.** \(2.5 \times 10^{-5} \text{ T}\)
- **B.** \(3.8 \times 10^{-5} \text{ T}\)
- **C.** \(5.0 \times 10^{-5} \text{ T}\)
- **D.** \(7.5 \times 10^{-5} \text{ T}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124879/*