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title: "Two long, parallel lines of charge are fixed at \\(x = -d\\) and \\(x = +d\\) in the \\(xy\\)-plane, carrying uniform linear charge densities \\(+\\lambda\\) and \\(-\\lambda\\), respectively. The electric potential is defined to be zero at the origin \\((0, 0)\\). Which of the following expressions gives the electric potential \\(V(x)\\) at a point along the \\(x\\)-axis in the region \\(-d < x < d\\)?"
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url: "https://nerd-notes.com/ubq/118149/"
date_modified: "2026-08-04T08:05:31+00:00"
---

# Two long, parallel lines of charge are fixed at \(x = -d\) and \(x = +d\) in the \(xy\)-plane, carrying uniform linear charge densities \(+\lambda\) and \(-\lambda\), respectively. The electric potential is defined to be zero at the origin \((0, 0)\). Which of the following expressions gives the electric potential \(V(x)\) at a point along the \(x\)-axis in the region \(-d < x < d\)?

Two long, parallel lines of charge are fixed at \(x = -d\) and \(x = +d\) in the \(xy\)-plane, carrying uniform linear charge densities \(+\lambda\) and \(-\lambda\), respectively. The electric potential is defined to be zero at the origin \((0, 0)\). Which of the following expressions gives the electric potential \(V(x)\) at a point along the \(x\)-axis in the region \(-d < x < d\)?

![A horizontal line represents the x-axis with an origin mark labeled 0 at the center. To the left of the origin at distance d, a vertical dashed line represents a line charge labeled with positive sign +\lambda at position x = -d. To the right of the origin at distance d, a vertical dashed line represents a line charge labeled with negative sign -\lambda at position x = +d. A point marked with a filled dot sits on the x-axis between the origin and x = +d, labeled x. A horizontal double-headed arrow below the axis extends from the origin to x = -d labeled d, and another horizontal double-headed arrow extends from the origin to x = +d labeled d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830731-hOVWmh.jpg)

- **A.** \(V(x) = \dfrac{\lambda}{2\pi \varepsilon_0} \ln\left(\dfrac{d + x}{d - x}\right)\)
- **B.** \(V(x) = \dfrac{\lambda}{2\pi \varepsilon_0} \ln\left(\dfrac{d - x}{d + x}\right)\)
- **C.** \(V(x) = \dfrac{\lambda}{4\pi \varepsilon_0} \ln\left(\dfrac{d - x}{d + x}\right)\)
- **D.** \(V(x) = \dfrac{\lambda}{2\pi \varepsilon_0} \ln\left(\dfrac{d^2 - x^2}{d^2}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118149/*