---
title: "A thin, nonconducting rod of length \\(L\\) lies along the \\(x\\)-axis with its left end at the origin \\(x = 0\\) and its right end at \\(x = L\\). The rod carries a non-uniform linear charge density given by \\(\\lambda(x) = \\alpha x\\), where \\(\\alpha\\) is a positive constant with appropriate units. Which of the following expressions gives the magnitude of the electric field at a point \\(P\\) on the \\(x\\)-axis located at \\(x = d\\), where \\(d > L\\)?"
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url: "https://nerd-notes.com/ubq/117939/"
date_modified: "2026-08-04T08:02:38+00:00"
---

# A thin, nonconducting rod of length \(L\) lies along the \(x\)-axis with its left end at the origin \(x = 0\) and its right end at \(x = L\). The rod carries a non-uniform linear charge density given by \(\lambda(x) = \alpha x\), where \(\alpha\) is a positive constant with appropriate units. Which of the following expressions gives the magnitude of the electric field at a point \(P\) on the \(x\)-axis located at \(x = d\), where \(d > L\)?

A thin, nonconducting rod of length \(L\) lies along the \(x\)-axis with its left end at the origin \(x = 0\) and its right end at \(x = L\). The rod carries a non-uniform linear charge density given by \(\lambda(x) = \alpha x\), where \(\alpha\) is a positive constant with appropriate units. Which of the following expressions gives the magnitude of the electric field at a point \(P\) on the \(x\)-axis located at \(x = d\), where \(d > L\)?

![A horizontal x-axis line extending from left to right with an origin labeled 0. A thick horizontal line segment representing a rod lies along the axis from x = 0 to x = L. A small shaded differential element of length dx is located along the rod at position x, with a distance arrow from the origin to this element labeled x. To the right of the rod at position x = d on the x-axis is a single point labeled P. A double-headed arrow above the axis shows the distance from the differential element at x to point P, labeled d - x. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830558-ZjSaj3.jpg)

- **A.** \(\dfrac{\alpha}{4\pi\varepsilon_0} \left[ \dfrac{L}{d - L} + \ln\left(1 - \dfrac{L}{d}\right) \right]\)
- **B.** \(\dfrac{\alpha}{4\pi\varepsilon_0} \left[ \dfrac{L}{d - L} - \ln\left(1 - \dfrac{L}{d}\right) \right]\)
- **C.** \(\dfrac{\alpha L^2}{8\pi\varepsilon_0 d(d - L)}\)
- **D.** \(\dfrac{\alpha L^2}{4\pi\varepsilon_0 d(d - L)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117939/*