---
title: "A thin, straight insulating rod of length \\(L\\) lies along the \\(x\\)-axis and is centered at the origin. The rod carries a uniform positive linear charge density \\(\\lambda\\). Which of the following definite integrals represents the electric potential \\(V\\) at a point \\(P\\) located at \\((0, y)\\) on the positive \\(y\\)-axis, relative to zero potential at infinity?"
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url: "https://nerd-notes.com/ubq/121064/"
date_modified: "2026-08-23T04:57:40+00:00"
---

# A thin, straight insulating rod of length \(L\) lies along the \(x\)-axis and is centered at the origin. The rod carries a uniform positive linear charge density \(\lambda\). Which of the following definite integrals represents the electric potential \(V\) at a point \(P\) located at \((0, y)\) on the positive \(y\)-axis, relative to zero potential at infinity?

A thin, straight insulating rod of length \(L\) lies along the \(x\)-axis and is centered at the origin. The rod carries a uniform positive linear charge density \(\lambda\). Which of the following definite integrals represents the electric potential \(V\) at a point \(P\) located at \((0, y)\) on the positive \(y\)-axis, relative to zero potential at infinity?

![A 2D Cartesian coordinate plane in grayscale showing a horizontal x-axis and a vertical y-axis intersecting at the origin (0,0). A thick horizontal line segment representing a charged rod lies along the x-axis, centered at the origin, extending symmetrically from x = -L/2 to x = L/2. Tick marks on the x-axis are labeled -L/2 and L/2. A point labeled P is marked with a small dot on the positive y-axis at coordinate (0, y). A small segment of width dx is highlighted on the rod at an arbitrary positive position x, and a straight dashed line labeled r extends from this element dx to point P. A label \lambda is positioned above the rod. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461060-8hJkEB.jpg)

- **A.** \(V = \dfrac{\lambda}{4\pi\varepsilon_0} \int_{-L/2}^{L/2} \dfrac{y}{x^2 + y^2}\,dx\)
- **B.** \(V = \dfrac{\lambda}{2\pi\varepsilon_0} \int_{0}^{L/2} \dfrac{1}{\sqrt{x^2 + y^2}}\,dx\)
- **C.** \(V = \dfrac{\lambda}{4\pi\varepsilon_0} \int_{0}^{L/2} \dfrac{1}{\sqrt{x^2 + y^2}}\,dx\)
- **D.** \(V = \dfrac{\lambda}{2\pi\varepsilon_0} \int_{0}^{L/2} \dfrac{y}{x^2 + y^2}\,dx\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121064/*