---
title: "A point charge \\(+q\\) is fixed on the \\(z\\)-axis at the coordinates \\((0, 0, d)\\), where \\(d > 0\\). A flat, nonconducting square plate with side length \\(2L\\) lies in the \\(xy\\)-plane and is centered at the origin, spanning the region \\(-L \\le x \\le L\\) and \\(-L \\le y \\le L\\). Which of the following expressions represents the magnitude of the electric flux passing through the plate?"
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url: "https://nerd-notes.com/ubq/124585/"
date_modified: "2026-09-28T14:08:45+00:00"
---

# A point charge \(+q\) is fixed on the \(z\)-axis at the coordinates \((0, 0, d)\), where \(d > 0\). A flat, nonconducting square plate with side length \(2L\) lies in the \(xy\)-plane and is centered at the origin, spanning the region \(-L \le x \le L\) and \(-L \le y \le L\). Which of the following expressions represents the magnitude of the electric flux passing through the plate?

A point charge \(+q\) is fixed on the \(z\)-axis at the coordinates \((0, 0, d)\), where \(d > 0\). A flat, nonconducting square plate with side length \(2L\) lies in the \(xy\)-plane and is centered at the origin, spanning the region \(-L \le x \le L\) and \(-L \le y \le L\). Which of the following expressions represents the magnitude of the electric flux passing through the plate?

![A three-dimensional Cartesian coordinate system shown in grayscale with three mutually perpendicular axes labeled \(x\), \(y\), and \(z\). The vertical axis is labeled \(z\) at its top arrow. The \(x\)-axis extends forward and to the left, and the \(y\)-axis extends to the right. A flat square plate lies entirely in the \(xy\)-plane, centered at the origin, with its edges parallel to the \(x\)- and \(y\)-axes. Tick marks on the \(x\)-axis are labeled \(-L\) and \(L\), and tick marks on the \(y\)-axis are labeled \(-L\) and \(L\). A filled black circle representing a point charge sits on the positive \(z\)-axis at a height labeled \(d\), with the text label \(+q\) adjacent to it. A straight dashed line segment connects the point charge to an arbitrary point \((x, y, 0)\) on the square plate. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604524-bBCvf5.jpg)

- **A.** \(\dfrac{qd}{4\pi\varepsilon_0} \int_{-L}^{L} \int_{-L}^{L} \dfrac{1}{(x^2 + y^2 + d^2)^{3/2}} \,dx\,dy\)
- **B.** \(\dfrac{q}{4\pi\varepsilon_0} \int_{-L}^{L} \int_{-L}^{L} \dfrac{1}{x^2 + y^2 + d^2} \,dx\,dy\)
- **C.** \(\dfrac{q}{4\pi\varepsilon_0} \int_{-L}^{L} \int_{-L}^{L} \dfrac{\sqrt{x^2 + y^2}}{(x^2 + y^2 + d^2)^{3/2}} \,dx\,dy\)
- **D.** \(\dfrac{qd}{4\pi\varepsilon_0} \int_{0}^{L} \int_{0}^{L} \dfrac{1}{(x^2 + y^2 + d^2)^{3/2}} \,dx\,dy\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124585/*