---
title: "A thin, nonconducting rod bent into a semicircle of radius \\(R\\) carries a total charge \\(Q\\) distributed uniformly along its length. A point charge \\(q\\) of the same sign as \\(Q\\) is held fixed at the center of curvature of the semicircle. Which of the following expressions is equal to the magnitude of the electrostatic force exerted on the point charge by the semicircular rod?"
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url: "https://nerd-notes.com/ubq/117922/"
date_modified: "2026-08-04T08:02:35+00:00"
---

# A thin, nonconducting rod bent into a semicircle of radius \(R\) carries a total charge \(Q\) distributed uniformly along its length. A point charge \(q\) of the same sign as \(Q\) is held fixed at the center of curvature of the semicircle. Which of the following expressions is equal to the magnitude of the electrostatic force exerted on the point charge by the semicircular rod?

A thin, nonconducting rod bent into a semicircle of radius \(R\) carries a total charge \(Q\) distributed uniformly along its length. A point charge \(q\) of the same sign as \(Q\) is held fixed at the center of curvature of the semicircle. Which of the following expressions is equal to the magnitude of the electrostatic force exerted on the point charge by the semicircular rod?

![A semicircular arc centered at the origin of an xy-plane lies entirely in the upper half-plane with a radius R extending from x = -R to x = +R. Small positive signs are spaced evenly along the arc to indicate uniform charge Q. A solid dot labeled q is located at the origin (0,0). A dashed line labeled R extends from the origin to a point on the arc. No other elements or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/semicircle-charge-setup-1785830555-ZSwELR.jpg)

- **A.** \(\dfrac{Qq}{4\pi \varepsilon_0 R^2}\)
- **B.** \(\dfrac{Qq}{2\pi^2 \varepsilon_0 R^2}\)
- **C.** \(\dfrac{Qq}{4\pi^2 \varepsilon_0 R^2}\)
- **D.** \(\dfrac{Qq}{\pi^2 \varepsilon_0 R^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117922/*