---
title: "A point charge \\(q\\) is located on the central symmetry axis of a flat circular disk of radius \\(R\\), at a distance \\(d\\) from the center of the disk. An open hemispherical surface shares the same circular boundary as the disk, forming a closed surface that encloses no electric charge. In terms of given quantities and fundamental constants, which of the following expressions represents the magnitude of the electric flux \\(\\Phi_E\\) through the open hemispherical surface?"
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url: "https://nerd-notes.com/ubq/118016/"
date_modified: "2026-08-04T08:02:56+00:00"
---

# A point charge \(q\) is located on the central symmetry axis of a flat circular disk of radius \(R\), at a distance \(d\) from the center of the disk. An open hemispherical surface shares the same circular boundary as the disk, forming a closed surface that encloses no electric charge. In terms of given quantities and fundamental constants, which of the following expressions represents the magnitude of the electric flux \(\Phi_E\) through the open hemispherical surface?

A point charge \(q\) is located on the central symmetry axis of a flat circular disk of radius \(R\), at a distance \(d\) from the center of the disk. An open hemispherical surface shares the same circular boundary as the disk, forming a closed surface that encloses no electric charge. In terms of given quantities and fundamental constants, which of the following expressions represents the magnitude of the electric flux \(\Phi_E\) through the open hemispherical surface?

![A point charge labeled q is located on a vertical dashed central axis at a distance d below a flat circular disk of radius R. The disk lies horizontally, shown in perspective as an ellipse with a dashed radius line labeled R from its center to its right edge. Attached to the circular boundary of the disk is a dome-shaped open hemispherical surface curving upward. The vertical distance from the point charge q to the center of the disk is labeled d. Arrows representing radial electric field lines radiate outward from the charge q, passing through both the disk and the open surface. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830575-iZqVr8.jpg)

- **A.** \(\dfrac{q}{\varepsilon_0}\left(1 - \dfrac{d}{\sqrt{R^2 + d^2}}\right)\)
- **B.** \(\dfrac{q}{2\varepsilon_0}\left(\dfrac{d}{\sqrt{R^2 + d^2}}\right)\)
- **C.** \(\dfrac{q}{2\varepsilon_0}\left(1 - \dfrac{d}{\sqrt{R^2 + d^2}}\right)\)
- **D.** \(\dfrac{q}{2\varepsilon_0}\left(1 - \dfrac{d^2}{R^2 + d^2}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118016/*