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title: "A thin, nonconducting rod of length \\(R\\) carries a total positive charge \\(Q\\) distributed uniformly along its length. The rod is centered at the origin of a coordinate system. Three concentric spherical Gaussian surfaces \\(S_1\\), \\(S_2\\), and \\(S_3\\) with radii \\(R\\), \\(2R\\), and \\(3R\\), respectively, are centered at the origin. Let \\(\\Phi_1\\), \\(\\Phi_2\\), and \\(\\Phi_3\\) represent the net electric flux through surfaces \\(S_1\\), \\(S_2\\), and \\(S_3\\), respectively. Which of the following correctly ranks the net electric fluxes through the three surfaces?"
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url: "https://nerd-notes.com/ubq/117924/"
date_modified: "2026-08-04T08:02:35+00:00"
---

# A thin, nonconducting rod of length \(R\) carries a total positive charge \(Q\) distributed uniformly along its length. The rod is centered at the origin of a coordinate system. Three concentric spherical Gaussian surfaces \(S_1\), \(S_2\), and \(S_3\) with radii \(R\), \(2R\), and \(3R\), respectively, are centered at the origin. Let \(\Phi_1\), \(\Phi_2\), and \(\Phi_3\) represent the net electric flux through surfaces \(S_1\), \(S_2\), and \(S_3\), respectively. Which of the following correctly ranks the net electric fluxes through the three surfaces?

A thin, nonconducting rod of length \(R\) carries a total positive charge \(Q\) distributed uniformly along its length. The rod is centered at the origin of a coordinate system. Three concentric spherical Gaussian surfaces \(S_1\), \(S_2\), and \(S_3\) with radii \(R\), \(2R\), and \(3R\), respectively, are centered at the origin. Let \(\Phi_1\), \(\Phi_2\), and \(\Phi_3\) represent the net electric flux through surfaces \(S_1\), \(S_2\), and \(S_3\), respectively. Which of the following correctly ranks the net electric fluxes through the three surfaces?

![A 2D cross-sectional diagram showing a thin horizontal rod centered at the origin (0,0). The rod has total length R, extending from x = -R/2 to x = +R/2, and is marked with plus signs indicating positive charge Q. Centered at the origin are three concentric dashed circles representing spherical surfaces: circle S_1 with radius R, circle S_2 with radius 2R, and circle S_3 with radius 3R. Radial arrows extending from the origin indicate the radii R, 2R, and 3R for each respective surface. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830555-h93itZ.jpg)

- **A.** \(\Phi_1 = \Phi_2 = \Phi_3\)
- **B.** \(\Phi_1 > \Phi_2 > \Phi_3\)
- **C.** \(\Phi_1 < \Phi_2 < \Phi_3\)
- **D.** \(\Phi_1 < \Phi_2 = \Phi_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117924/*