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title: "Three long cylindrical conductors, each of radius \\(R\\), carry the same total current \\(I\\) distributed symmetrically about their central longitudinal axes.  The table shows the measured magnetic field magnitude \\(B(r)\\) as a function of radial distance \\(r\\) from the central axis for each cylinder, where \\(B_0 = \\dfrac{\\mu_0 I}{2\\pi R}\\).  | Radial Distance | Cylinder 1 | Cylinder 2 | Cylinder 3 | | :— | :— | :— | :— | | \\(r = 0.5R\\) | \\(0\\) | \\(0.5B_0\\) | \\(0.25B_0\\) | | \\(r = R\\) | \\(B_0\\) | \\(B_0\\) | \\(B_0\\) | | \\(r = 2R\\) | \\(0.5B_0\\) | \\(0.5B_0\\) | \\(0.5B_0\\) |  Which of the following correctly classifies the current distribution inside each cylinder for \\(r \\le R\\)?"
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url: "https://nerd-notes.com/ubq/124846/"
date_modified: "2026-09-28T14:11:39+00:00"
---

# Three long cylindrical conductors, each of radius \(R\), carry the same total current \(I\) distributed symmetrically about their central longitudinal axes.

The table shows the measured magnetic field magnitude \(B(r)\) as a function of radial distance \(r\) from the central axis for each cylinder, where \(B_0 = \dfrac{\mu_0 I}{2\pi R}\).

| Radial Distance | Cylinder 1 | Cylinder 2 | Cylinder 3 |
| :— | :— | :— | :— |
| \(r = 0.5R\) | \(0\) | \(0.5B_0\) | \(0.25B_0\) |
| \(r = R\) | \(B_0\) | \(B_0\) | \(B_0\) |
| \(r = 2R\) | \(0.5B_0\) | \(0.5B_0\) | \(0.5B_0\) |

Which of the following correctly classifies the current distribution inside each cylinder for \(r \le R\)?

Three long cylindrical conductors, each of radius \(R\), carry the same total current \(I\) distributed symmetrically about their central longitudinal axes.

The table shows the measured magnetic field magnitude \(B(r)\) as a function of radial distance \(r\) from the central axis for each cylinder, where \(B_0 = \dfrac{\mu_0 I}{2\pi R}\).

| Radial Distance | Cylinder 1 | Cylinder 2 | Cylinder 3 |
| :--- | :--- | :--- | :--- |
| \(r = 0.5R\) | \(0\) | \(0.5B_0\) | \(0.25B_0\) |
| \(r = R\) | \(B_0\) | \(B_0\) | \(B_0\) |
| \(r = 2R\) | \(0.5B_0\) | \(0.5B_0\) | \(0.5B_0\) |

Which of the following correctly classifies the current distribution inside each cylinder for \(r \le R\)?

- **A.** | Cylinder 1 | Cylinder 2 | Cylinder 3 | | :--- | :--- | :--- | | Surface current only | Uniform volume current density | Volume current density proportional to \(r\) |
- **B.** | Cylinder 1 | Cylinder 2 | Cylinder 3 | | :--- | :--- | :--- | | Surface current only | Volume current density proportional to \(r\) | Volume current density proportional to \(r^2\) |
- **C.** | Cylinder 1 | Cylinder 2 | Cylinder 3 | | :--- | :--- | :--- | | Surface current only | Uniform volume current density | Volume current density proportional to \(r^2\) |
- **D.** | Cylinder 1 | Cylinder 2 | Cylinder 3 | | :--- | :--- | :--- | | Current along central axis only | Uniform volume current density | Volume current density proportional to \(r\) |

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124846/*