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title: "A point charge \\(+q\\) is initially held at a distance \\(d\\) from a large, grounded flat conducting plate. The electric field in the region in front of the plate is identical to the field produced by charge \\(+q\\) and an image charge \\(-q\\) located at a distance \\(d\\) behind the plane of the plate (a total separation of \\(2d\\)). An external agent slowly moves the charge \\(+q\\) directly away from the plate, increasing its distance from \\(x = d\\) to \\(x = 3d\\). Which of the following expressions represents the work done by the external agent on the charge during this process?"
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url: "https://nerd-notes.com/ubq/118312/"
date_modified: "2026-08-04T08:08:58+00:00"
---

# A point charge \(+q\) is initially held at a distance \(d\) from a large, grounded flat conducting plate. The electric field in the region in front of the plate is identical to the field produced by charge \(+q\) and an image charge \(-q\) located at a distance \(d\) behind the plane of the plate (a total separation of \(2d\)). An external agent slowly moves the charge \(+q\) directly away from the plate, increasing its distance from \(x = d\) to \(x = 3d\). Which of the following expressions represents the work done by the external agent on the charge during this process?

A point charge \(+q\) is initially held at a distance \(d\) from a large, grounded flat conducting plate. The electric field in the region in front of the plate is identical to the field produced by charge \(+q\) and an image charge \(-q\) located at a distance \(d\) behind the plane of the plate (a total separation of \(2d\)). An external agent slowly moves the charge \(+q\) directly away from the plate, increasing its distance from \(x = d\) to \(x = 3d\). Which of the following expressions represents the work done by the external agent on the charge during this process?

![A vertical grounded conducting plate is drawn as a thick shaded rectangle along the vertical axis at x = 0. To the right of the plate at a horizontal distance d, a small solid circle labeled +q represents a point charge. To the left of the plate at a horizontal distance d inside a dashed region, a dashed circle labeled -q represents an image charge. A horizontal axis labeled x extends perpendicular to the plate. An arrow pointing to the right from +q indicates displacement toward x = 3d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830938-hyMGkM.jpg)

- **A.** \(\dfrac{q^2}{48\pi\varepsilon_0 d}\)
- **B.** \(\dfrac{q^2}{24\pi\varepsilon_0 d}\)
- **C.** \(\dfrac{q^2}{12\pi\varepsilon_0 d}\)
- **D.** \(\dfrac{q^2}{6\pi\varepsilon_0 d}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118312/*