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title: "A thin, flat, nonconducting square sheet with side length \\(L\\) lies in the \\(xy\\)-plane and carries a uniform positive surface charge density \\(\\sigma\\). A student wishes to apply Gauss’s law to determine the magnitude of the electric field at a point located at a distance \\(z \\ll L\\) from the center of the sheet. Which of the following diagrams correctly shows the orientation of a cylindrical Gaussian surface of cross-sectional area \\(A\\) and the electric field vectors \\(\\vec{E}\\) such that the electric flux through the curved surface is zero and the electric flux is nonzero only through the flat end-caps?"
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url: "https://nerd-notes.com/ubq/124713/"
date_modified: "2026-09-28T14:09:14+00:00"
---

# A thin, flat, nonconducting square sheet with side length \(L\) lies in the \(xy\)-plane and carries a uniform positive surface charge density \(\sigma\). A student wishes to apply Gauss’s law to determine the magnitude of the electric field at a point located at a distance \(z \ll L\) from the center of the sheet. Which of the following diagrams correctly shows the orientation of a cylindrical Gaussian surface of cross-sectional area \(A\) and the electric field vectors \(\vec{E}\) such that the electric flux through the curved surface is zero and the electric flux is nonzero only through the flat end-caps?

A thin, flat, nonconducting square sheet with side length \(L\) lies in the \(xy\)-plane and carries a uniform positive surface charge density \(\sigma\). A student wishes to apply Gauss's law to determine the magnitude of the electric field at a point located at a distance \(z \ll L\) from the center of the sheet. Which of the following diagrams correctly shows the orientation of a cylindrical Gaussian surface of cross-sectional area \(A\) and the electric field vectors \(\vec{E}\) such that the electric flux through the curved surface is zero and the electric flux is nonzero only through the flat end-caps?

![A perspective view of a flat square sheet lying horizontally in an oblique projection. The square sheet is shaded light gray with four straight outer edges, each of length labeled \(L\). At the center of the top face of the sheet is a label \(+\sigma\). A vertical dashed centerline passes perpendicularly through the geometric center of the sheet, extending upward and downward. A single straight arrow labeled \(z\) points vertically upward along this centerline from the center of the sheet. At the bottom-left corner of the sheet, a set of Cartesian coordinate axes shows a horizontal axis pointing right labeled \(x\), an oblique axis pointing forward-left labeled \(y\), and a vertical axis pointing upward labeled \(z\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604552-1XUozh.jpg)

- **A.** Diagram A
- **B.** Diagram B
- **C.** Diagram C
- **D.** Diagram D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124713/*