---
title: "A long electrostatic system consists of concentric cylindrical regions centered on the z-axis. The electric field is directed radially outward, with magnitude \\(E(r) = 0\\) for \\(0 \\le r < R\\), \\(E(r) \\propto 1/r\\) for \\(R < r < 2R\\), \\(E(r) = 0\\) for \\(2R < r  3R\\), as shown in the graph. Which of the following statements correctly describes the physical properties of the system based on this field profile?"
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url: "https://nerd-notes.com/ubq/124535/"
date_modified: "2026-09-28T14:08:33+00:00"
---

# A long electrostatic system consists of concentric cylindrical regions centered on the z-axis. The electric field is directed radially outward, with magnitude \(E(r) = 0\) for \(0 \le r < R\), \(E(r) \propto 1/r\) for \(R < r < 2R\), \(E(r) = 0\) for \(2R < r  3R\), as shown in the graph. Which of the following statements correctly describes the physical properties of the system based on this field profile?

A long electrostatic system consists of concentric cylindrical regions centered on the z-axis. The electric field is directed radially outward, with magnitude \(E(r) = 0\) for \(0 \le r < R\), \(E(r) \propto 1/r\) for \(R < r < 2R\), \(E(r) = 0\) for \(2R < r < 3R\), and \(E(r) \propto 1/r\) for \(r > 3R\), as shown in the graph. Which of the following statements correctly describes the physical properties of the system based on this field profile?

![A line graph showing the radial electric field magnitude E as a function of radial distance r. The horizontal axis is labeled r and has tick marks at the origin 0, R, 2R, and 3R. The vertical axis is labeled E and has a tick mark labeled E_0. From r = 0 to r = R, a heavy solid line lies along the horizontal axis at E = 0. At r = R, a vertical dashed line extends upward from the axis to a height E_0. From r = R to r = 2R, a solid curve decreases smoothly with upward concavity from (R, E_0) to (2R, E_0/2). At r = 2R, a vertical dashed line drops from (2R, E_0/2) to the horizontal axis. From r = 2R to r = 3R, a heavy solid line lies along the horizontal axis at E = 0. At r = 3R, a vertical dashed line rises from the axis to a height of E_0/3, and a solid curve decreases smoothly with upward concavity toward the horizontal axis for r > 3R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604513-ouoVLJ.jpg)

- **A.** The electric potential is zero throughout the region \(0 \le r < R\) because the electric field is zero in the bulk of the inner conductor.
- **B.** The region \(R < r < 2R\) is occupied by a conducting material because the electric field continuously decreases toward zero as \(r\) increases.
- **C.** The region \(2R < r < 3R\) is a conducting shell throughout which the electric potential is constant, and a negative surface charge resides at the boundary \(r = 2R\).
- **D.** The cylindrical shell in the region \(2R < r < 3R\) must carry zero net charge because the electric field is zero everywhere within that region.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124535/*