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title: "Four point charges are fixed in the \\(xy\\)-plane on the coordinate axes at a distance \\(a\\) from the origin, as shown in the figure. Two positive charges \\(+q\\) are located at \\((a,0)\\) and \\((-a,0)\\), and two negative charges \\(-q\\) are located at \\((0,a)\\) and \\((0,-a)\\). A point \\(P\\) is located on the positive \\(x\\)-axis at position \\(x = x_0\\), where \\(x_0 \\gg a\\). Assuming electric potential is zero at infinity, which of the following expressions best approximates the electric potential \\(V\\) at point \\(P\\)?"
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url: "https://nerd-notes.com/ubq/118101/"
date_modified: "2026-08-04T08:05:07+00:00"
---

# Four point charges are fixed in the \(xy\)-plane on the coordinate axes at a distance \(a\) from the origin, as shown in the figure. Two positive charges \(+q\) are located at \((a,0)\) and \((-a,0)\), and two negative charges \(-q\) are located at \((0,a)\) and \((0,-a)\). A point \(P\) is located on the positive \(x\)-axis at position \(x = x_0\), where \(x_0 \gg a\). Assuming electric potential is zero at infinity, which of the following expressions best approximates the electric potential \(V\) at point \(P\)?

Four point charges are fixed in the \(xy\)-plane on the coordinate axes at a distance \(a\) from the origin, as shown in the figure. Two positive charges \(+q\) are located at \((a,0)\) and \((-a,0)\), and two negative charges \(-q\) are located at \((0,a)\) and \((0,-a)\). A point \(P\) is located on the positive \(x\)-axis at position \(x = x_0\), where \(x_0 \gg a\). Assuming electric potential is zero at infinity, which of the following expressions best approximates the electric potential \(V\) at point \(P\)?

![A Cartesian coordinate system showing x-axis and y-axis. Four point charges are placed on the axes at a distance a from the origin: a positive charge labeled +q at (a,0), a negative charge labeled -q at (0,a), a positive charge labeled +q at (-a,0), and a negative charge labeled -q at (0,-a). A point labeled P is located on the positive x-axis at x_0, where x_0 is much larger than a. Dashed line segments connect the origin to each of the four charges, labeled a. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830707-FOZWvc.jpg)

- **A.** \(\dfrac{q a^2}{4\pi\varepsilon_0 x_0^3}\)
- **B.** \(\dfrac{q a^2}{2\pi\varepsilon_0 x_0^3}\)
- **C.** \(\dfrac{3 q a^2}{4\pi\varepsilon_0 x_0^3}\)
- **D.** \(\dfrac{q a}{2\pi\varepsilon_0 x_0^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118101/*