---
title: "A very long, hollow cylindrical conductor has an inner radius \\(a\\) and an outer radius \\(b\\). The conductor carries a steady current directed parallel to its central axis with a non-uniform volume current density given by \\(J(r) = \\dfrac{C_0}{r}\\) for \\(a \\le r \\le b\\), where \\(C_0\\) is a positive constant and \\(r\\) is the radial distance from the central axis. The region \\(r  b\\)?"
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url: "https://nerd-notes.com/ubq/121282/"
date_modified: "2026-08-23T04:59:24+00:00"
---

# A very long, hollow cylindrical conductor has an inner radius \(a\) and an outer radius \(b\). The conductor carries a steady current directed parallel to its central axis with a non-uniform volume current density given by \(J(r) = \dfrac{C_0}{r}\) for \(a \le r \le b\), where \(C_0\) is a positive constant and \(r\) is the radial distance from the central axis. The region \(r  b\)?

A very long, hollow cylindrical conductor has an inner radius \(a\) and an outer radius \(b\). The conductor carries a steady current directed parallel to its central axis with a non-uniform volume current density given by \(J(r) = \dfrac{C_0}{r}\) for \(a \le r \le b\), where \(C_0\) is a positive constant and \(r\) is the radial distance from the central axis. The region \(r < a\) is empty space. Which of the following graphs best represents the magnitude of the magnetic field \(B\) as a function of \(r\) from \(r = 0\) to \(r > b\)?

![A cross-sectional view of a thick cylindrical shell centered at the origin. A dashed horizontal line and a dashed vertical line intersect at the center. An inner circle of radius \(a\) is drawn with a solid line, with an arrow labeled \(a\) extending from the center to the inner boundary at 135 degrees. An outer circle of radius \(b\) is drawn with a solid line, with an arrow labeled \(b\) extending from the center to the outer boundary at 45 degrees. The annular region between radius \(a\) and radius \(b\) is shaded light gray and contains eight evenly spaced circled-dot symbols representing current directed out of the page. The interior region inside radius \(a\) is unshaded white. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-cross-section-1787461162-pnDpU7.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121282/*