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title: "Two point charges, \\(+q\\) and \\(-q\\), are held fixed on the \\(x\\)-axis at coordinates \\(x = -d\\) and \\(x = +d\\), respectively, where \\(d > 0\\). The electric potential is defined to be zero at an infinite distance from the charges, and the unit vector \\(\\hat{i}\\) points in the \\(+x\\)-direction. Which row in the table correctly identifies the net electric potential \\(V\\) and the net electric field vector \\(\\vec{E}\\) at the origin \\(P(0,0)\\)?  | | Net Electric Potential \\(V\\) | Net Electric Field Vector \\(\\vec{E}\\) | |—|—|—| | Row A | \\(\\dfrac{q}{2\\pi\\varepsilon_0 d}\\) | \\(\\vec{0}\\) | | Row B | \\(\\dfrac{q}{2\\pi\\varepsilon_0 d}\\) | \\(\\dfrac{q}{2\\pi\\varepsilon_0 d^2}\\hat{i}\\) | | Row C | \\(0\\) | \\(\\vec{0}\\) | | Row D | \\(0\\) | \\(\\dfrac{q}{2\\pi\\varepsilon_0 d^2}\\hat{i}\\) |"
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url: "https://nerd-notes.com/ubq/121087/"
date_modified: "2026-08-23T04:57:47+00:00"
---

# Two point charges, \(+q\) and \(-q\), are held fixed on the \(x\)-axis at coordinates \(x = -d\) and \(x = +d\), respectively, where \(d > 0\). The electric potential is defined to be zero at an infinite distance from the charges, and the unit vector \(\hat{i}\) points in the \(+x\)-direction. Which row in the table correctly identifies the net electric potential \(V\) and the net electric field vector \(\vec{E}\) at the origin \(P(0,0)\)?

| | Net Electric Potential \(V\) | Net Electric Field Vector \(\vec{E}\) |
|—|—|—|
| Row A | \(\dfrac{q}{2\pi\varepsilon_0 d}\) | \(\vec{0}\) |
| Row B | \(\dfrac{q}{2\pi\varepsilon_0 d}\) | \(\dfrac{q}{2\pi\varepsilon_0 d^2}\hat{i}\) |
| Row C | \(0\) | \(\vec{0}\) |
| Row D | \(0\) | \(\dfrac{q}{2\pi\varepsilon_0 d^2}\hat{i}\) |

Two point charges, \(+q\) and \(-q\), are held fixed on the \(x\)-axis at coordinates \(x = -d\) and \(x = +d\), respectively, where \(d > 0\). The electric potential is defined to be zero at an infinite distance from the charges, and the unit vector \(\hat{i}\) points in the \(+x\)-direction. Which row in the table correctly identifies the net electric potential \(V\) and the net electric field vector \(\vec{E}\) at the origin \(P(0,0)\)?

| | Net Electric Potential \(V\) | Net Electric Field Vector \(\vec{E}\) |
|---|---|---|
| Row A | \(\dfrac{q}{2\pi\varepsilon_0 d}\) | \(\vec{0}\) |
| Row B | \(\dfrac{q}{2\pi\varepsilon_0 d}\) | \(\dfrac{q}{2\pi\varepsilon_0 d^2}\hat{i}\) |
| Row C | \(0\) | \(\vec{0}\) |
| Row D | \(0\) | \(\dfrac{q}{2\pi\varepsilon_0 d^2}\hat{i}\) |

![A horizontal line representing the \(x\)-axis with an arrow on the right end labeled \(x\). At the center of the line, a small solid black dot is labeled \(P\) and \(0\) below the axis. To the left of \(P\), at a marked position \(-d\), there is a circle with a plus sign inside labeled \(+q\) above it. To the right of \(P\), at an equal distance marked position \(+d\), there is an identical circle with a minus sign inside labeled \(-q\) above it. Two double-ended horizontal dimension arrows below the axis indicate the distance \(d\) from \(-d\) to \(0\) labeled \(d\), and the distance from \(0\) to \(+d\) labeled \(d\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461067-YPnSqv.jpg)

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121087/*