---
title: "Two thin, nonconducting curved rods are bent into circular arcs, each having the same radius of curvature \\(R\\) and carrying the same total positive charge \\(Q\\) distributed uniformly along its length. Arc 1 subtends an angle of \\(90^\\circ\\) (\\(\\pi/2\\text{ rad}\\)) at its center of curvature, while Arc 2 subtends an angle of \\(60^\\circ\\) (\\(\\pi/3\\text{ rad}\\)) at its center of curvature. What is the ratio of the magnitude of the electric field at the center of curvature due to Arc 1 to that due to Arc 2, \\(E_1 / E_2\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/124551/"
date_modified: "2026-09-28T14:08:36+00:00"
---

# Two thin, nonconducting curved rods are bent into circular arcs, each having the same radius of curvature \(R\) and carrying the same total positive charge \(Q\) distributed uniformly along its length. Arc 1 subtends an angle of \(90^\circ\) (\(\pi/2\text{ rad}\)) at its center of curvature, while Arc 2 subtends an angle of \(60^\circ\) (\(\pi/3\text{ rad}\)) at its center of curvature. What is the ratio of the magnitude of the electric field at the center of curvature due to Arc 1 to that due to Arc 2, \(E_1 / E_2\)?

Two thin, nonconducting curved rods are bent into circular arcs, each having the same radius of curvature \(R\) and carrying the same total positive charge \(Q\) distributed uniformly along its length. Arc 1 subtends an angle of \(90^\circ\) (\(\pi/2\text{ rad}\)) at its center of curvature, while Arc 2 subtends an angle of \(60^\circ\) (\(\pi/3\text{ rad}\)) at its center of curvature. What is the ratio of the magnitude of the electric field at the center of curvature due to Arc 1 to that due to Arc 2, \(E_1 / E_2\)?

![Two side-by-side circular arcs, Arc 1 on the left and Arc 2 on the right, each with a center of curvature marked by a dot labeled O. Arc 1 spans 90 degrees symmetrically across a vertical dashed line, with an arrow labeled R pointing from O to the midpoint of the arc, and a label Q beside the arc. Arc 2 spans 60 degrees symmetrically across a vertical dashed line, with an arrow labeled R pointing from O to the midpoint of the arc, and a label Q beside the arc. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604516-L5VxX1.jpg)

- **A.** \(\dfrac{2}{3}\)
- **B.** \(\dfrac{2\sqrt{2}}{3}\)
- **C.** \(\dfrac{3\sqrt{2}}{4}\)
- **D.** \(\sqrt{2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124551/*