---
title: "A solid sphere of radius \\(R\\), an infinitely long solid cylinder of radius \\(R\\), and an infinite slab of thickness \\(2R\\) each carry a uniform positive volume charge density \\(\\rho_0\\).  The distance \\(r\\) is measured from the center of the sphere, from the central symmetry axis of the cylinder, and from the central midplane of the slab, respectively.  | Row | Inside all three (\\(r  R\\)) | Outside cylinder (\\(r > R\\)) | Outside slab (\\(r > R\\)) | | :—: | :—: | :—: | :—: | :—: | | A | Zero | Proportional to \\(1/r^2\\) | Proportional to \\(1/r\\) | Independent of \\(r\\) | | B | Proportional to \\(r\\) | Proportional to \\(1/r\\) | Proportional to \\(1/r^2\\) | Independent of \\(r\\) | | C | Proportional to \\(r\\) | Proportional to \\(1/r^2\\) | Proportional to \\(1/r\\) | Independent of \\(r\\) | | D | Proportional to \\(r\\) | Proportional to \\(1/r^2\\) | Independent of \\(r\\) | Proportional to \\(1/r\\) |  Which row in the table correctly identifies the functional dependence of the electric field magnitude \\(E(r)\\) on \\(r\\) for all three configurations in the region \\(r  R\\)?"
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url: "https://nerd-notes.com/ubq/124616/"
date_modified: "2026-09-28T14:08:51+00:00"
---

# A solid sphere of radius \(R\), an infinitely long solid cylinder of radius \(R\), and an infinite slab of thickness \(2R\) each carry a uniform positive volume charge density \(\rho_0\).

The distance \(r\) is measured from the center of the sphere, from the central symmetry axis of the cylinder, and from the central midplane of the slab, respectively.

| Row | Inside all three (\(r  R\)) | Outside cylinder (\(r > R\)) | Outside slab (\(r > R\)) |
| :—: | :—: | :—: | :—: | :—: |
| A | Zero | Proportional to \(1/r^2\) | Proportional to \(1/r\) | Independent of \(r\) |
| B | Proportional to \(r\) | Proportional to \(1/r\) | Proportional to \(1/r^2\) | Independent of \(r\) |
| C | Proportional to \(r\) | Proportional to \(1/r^2\) | Proportional to \(1/r\) | Independent of \(r\) |
| D | Proportional to \(r\) | Proportional to \(1/r^2\) | Independent of \(r\) | Proportional to \(1/r\) |

Which row in the table correctly identifies the functional dependence of the electric field magnitude \(E(r)\) on \(r\) for all three configurations in the region \(r  R\)?

A solid sphere of radius \(R\), an infinitely long solid cylinder of radius \(R\), and an infinite slab of thickness \(2R\) each carry a uniform positive volume charge density \(\rho_0\).

The distance \(r\) is measured from the center of the sphere, from the central symmetry axis of the cylinder, and from the central midplane of the slab, respectively.

| Row | Inside all three (\(r < R\)) | Outside sphere (\(r > R\)) | Outside cylinder (\(r > R\)) | Outside slab (\(r > R\)) |
| :---: | :---: | :---: | :---: | :---: |
| A | Zero | Proportional to \(1/r^2\) | Proportional to \(1/r\) | Independent of \(r\) |
| B | Proportional to \(r\) | Proportional to \(1/r\) | Proportional to \(1/r^2\) | Independent of \(r\) |
| C | Proportional to \(r\) | Proportional to \(1/r^2\) | Proportional to \(1/r\) | Independent of \(r\) |
| D | Proportional to \(r\) | Proportional to \(1/r^2\) | Independent of \(r\) | Proportional to \(1/r\) |

Which row in the table correctly identifies the functional dependence of the electric field magnitude \(E(r)\) on \(r\) for all three configurations in the region \(r < R\) and for each individual configuration in the region \(r > R\)?

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124616/*