---
title: "Two fixed point charges are positioned on the \\(x\\)-axis: charge \\(q_1 = +3Q\\) at \\(x = -d\\) and charge \\(q_2 = -Q\\) at \\(x = +d\\). A third point charge \\(+q\\) is initially located at the origin \\(x = 0\\). An external agent slowly moves charge \\(+q\\) from the origin to point \\(P\\) located at \\(x = +3d\\). Which of the following expressions represents the work done by the external agent on charge \\(+q\\) during this process?"
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url: "https://nerd-notes.com/ubq/117463/"
date_modified: "2026-08-04T06:52:14+00:00"
---

# Two fixed point charges are positioned on the \(x\)-axis: charge \(q_1 = +3Q\) at \(x = -d\) and charge \(q_2 = -Q\) at \(x = +d\). A third point charge \(+q\) is initially located at the origin \(x = 0\). An external agent slowly moves charge \(+q\) from the origin to point \(P\) located at \(x = +3d\). Which of the following expressions represents the work done by the external agent on charge \(+q\) during this process?

Two fixed point charges are positioned on the \(x\)-axis: charge \(q_1 = +3Q\) at \(x = -d\) and charge \(q_2 = -Q\) at \(x = +d\). A third point charge \(+q\) is initially located at the origin \(x = 0\). An external agent slowly moves charge \(+q\) from the origin to point \(P\) located at \(x = +3d\). Which of the following expressions represents the work done by the external agent on charge \(+q\) during this process?

![A horizontal x-axis with an origin marker labeled 0. On the x-axis, a positive point charge labeled q_1 = +3Q sits at x = -d. A negative point charge labeled q_2 = -Q sits at x = +d. Axis tick marks are spaced at uniform intervals of d, labeled -d, 0, +d, +2d, and +3d. A positive test charge labeled +q is positioned at the origin 0, with a horizontal dashed line extending from 0 to a target point labeled P at x = +3d. A arrow labeled external force points rightward along the dashed path toward P. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826333-GyySmh.jpg)

- **A.** \(-\dfrac{11kQq}{4d}\)
- **B.** \(-\dfrac{3kQq}{2d}\)
- **C.** \(-\dfrac{7kQq}{4d}\)
- **D.** \(+\dfrac{7kQq}{4d}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117463/*