---
title: "Three point charges are fixed along the \\(x\\)-axis: a charge \\(-2q\\) is located at the origin, and two charges each of charge \\(+q\\) are located at \\(x = -d\\) and \\(x = +d\\). Point \\(P\\) lies on the positive \\(y\\)-axis at a distance \\(y\\) from the origin. Which of the following expressions represents the magnitude of the net electric field at point \\(P\\) in terms of given quantities and fundamental constants?"
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url: "https://nerd-notes.com/ubq/117907/"
date_modified: "2026-08-04T08:02:32+00:00"
---

# Three point charges are fixed along the \(x\)-axis: a charge \(-2q\) is located at the origin, and two charges each of charge \(+q\) are located at \(x = -d\) and \(x = +d\). Point \(P\) lies on the positive \(y\)-axis at a distance \(y\) from the origin. Which of the following expressions represents the magnitude of the net electric field at point \(P\) in terms of given quantities and fundamental constants?

Three point charges are fixed along the \(x\)-axis: a charge \(-2q\) is located at the origin, and two charges each of charge \(+q\) are located at \(x = -d\) and \(x = +d\). Point \(P\) lies on the positive \(y\)-axis at a distance \(y\) from the origin. Which of the following expressions represents the magnitude of the net electric field at point \(P\) in terms of given quantities and fundamental constants?

![A 2D schematic diagram in the xy-plane. A horizontal dashed coordinate axis is labeled x, and a vertical dashed coordinate axis is labeled y, intersecting at the origin labeled O. On the x-axis, three point charges are shown: a charge labeled -2q at the origin O, a charge labeled +q located at x = -d, and a charge labeled +q located at x = +d. A point labeled P is positioned on the positive y-axis at a distance y from the origin O. Two thin dashed lines connect the point P to the charge at x = -d and to the charge at x = +d. A double-headed dimension arrow indicates the distance d from the origin to each +q charge, and another double-headed dimension arrow indicates the distance y from the origin to point P. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830552-gPOU0n.jpg)

- **A.** \(\dfrac{q}{2\pi\varepsilon_0} \left( \dfrac{1}{y^2} - \dfrac{y}{(y^2 + d^2)^{3/2}} \right)\)
- **B.** \(\dfrac{q}{2\pi\varepsilon_0} \left( \dfrac{1}{y^2} - \dfrac{1}{y^2 + d^2} \right)\)
- **C.** \(\dfrac{q}{2\pi\varepsilon_0} \left( \dfrac{1}{y^2} + \dfrac{y}{(y^2 + d^2)^{3/2}} \right)\)
- **D.** \(\dfrac{q}{4\pi\varepsilon_0} \left( \dfrac{1}{y^2} - \dfrac{d}{(y^2 + d^2)^{3/2}} \right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117907/*