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title: "A thin, nonconducting rod of length \\(L\\) lies along the \\(x\\)-axis from \\(x = -L/2\\) to \\(x = L/2\\) and carries a total positive charge \\(Q\\) distributed uniformly along its length. Point \\(P\\) is located on the positive \\(y\\)-axis at a distance \\(y\\) from the origin, as shown in the figure. Assuming the electric potential is defined to be zero at infinity, which of the following expressions represents the electric potential \\(V\\) at point \\(P\\)?"
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url: "https://nerd-notes.com/ubq/118112/"
date_modified: "2026-08-04T08:05:12+00:00"
---

# A thin, nonconducting rod of length \(L\) lies along the \(x\)-axis from \(x = -L/2\) to \(x = L/2\) and carries a total positive charge \(Q\) distributed uniformly along its length. Point \(P\) is located on the positive \(y\)-axis at a distance \(y\) from the origin, as shown in the figure. Assuming the electric potential is defined to be zero at infinity, which of the following expressions represents the electric potential \(V\) at point \(P\)?

A thin, nonconducting rod of length \(L\) lies along the \(x\)-axis from \(x = -L/2\) to \(x = L/2\) and carries a total positive charge \(Q\) distributed uniformly along its length. Point \(P\) is located on the positive \(y\)-axis at a distance \(y\) from the origin, as shown in the figure. Assuming the electric potential is defined to be zero at infinity, which of the following expressions represents the electric potential \(V\) at point \(P\)?

![A Cartesian coordinate system with a horizontal x-axis and a vertical y-axis meeting at origin (0,0). A thin horizontal rod of length L lies along the x-axis, extending from x = -L/2 to x = L/2. Point P is located on the positive y-axis at distance y from the origin, labeled P(0,y). A small differential segment of length dx is highlighted on the x-axis at coordinate x, labeled with charge dq. A straight dashed line segment connects this differential segment dq to point P and is labeled r. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830712-vyt3eG.jpg)

- **A.** \(V = \dfrac{Q}{4\pi\varepsilon_0 L} \int_{-L/2}^{L/2} \dfrac{y}{(x^2 + y^2)^{3/2}} \, dx\)
- **B.** \(V = \dfrac{Q}{4\pi\varepsilon_0 L} \int_{-L/2}^{L/2} \dfrac{1}{x^2 + y^2} \, dx\)
- **C.** \(V = \dfrac{Q}{4\pi\varepsilon_0 L} \int_{-L/2}^{L/2} \dfrac{y}{\sqrt{x^2 + y^2}} \, dx\)
- **D.** \(V = \dfrac{Q}{4\pi\varepsilon_0 L} \int_{-L/2}^{L/2} \dfrac{1}{\sqrt{x^2 + y^2}} \, dx\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118112/*