---
title: "A flat circular coil consists of \\(N\\) tightly wound turns of wire, has radius \\(r\\), and has total electrical resistance \\(R\\). The coil lies initially in the \\(xy\\)-plane within a uniform, constant magnetic field \\(\\vec{B} = B_0 \\hat{k}\\). The coil is then rotated by \\(180^\\circ\\) at a constant angular speed \\(\\omega\\) about a fixed diameter parallel to the \\(x\\)-axis. Which of the following expressions represents the total magnitude of electric charge \\(Q\\) that passes through any cross-section of the wire during this rotation?"
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url: "https://nerd-notes.com/ubq/118706/"
date_modified: "2026-08-04T08:13:49+00:00"
---

# A flat circular coil consists of \(N\) tightly wound turns of wire, has radius \(r\), and has total electrical resistance \(R\). The coil lies initially in the \(xy\)-plane within a uniform, constant magnetic field \(\vec{B} = B_0 \hat{k}\). The coil is then rotated by \(180^\circ\) at a constant angular speed \(\omega\) about a fixed diameter parallel to the \(x\)-axis. Which of the following expressions represents the total magnitude of electric charge \(Q\) that passes through any cross-section of the wire during this rotation?

A flat circular coil consists of \(N\) tightly wound turns of wire, has radius \(r\), and has total electrical resistance \(R\). The coil lies initially in the \(xy\)-plane within a uniform, constant magnetic field \(\vec{B} = B_0 \hat{k}\). The coil is then rotated by \(180^\circ\) at a constant angular speed \(\omega\) about a fixed diameter parallel to the \(x\)-axis. Which of the following expressions represents the total magnitude of electric charge \(Q\) that passes through any cross-section of the wire during this rotation?

![A 3D perspective diagram showing a circular loop of wire with radius r sitting flat in the xy-plane. Three parallel vertical arrows labeled B_0 point upward in the +z direction passing perpendicularly through the interior of the loop. A dashed line passes horizontally through the center of the loop along the x-axis, representing the axis of rotation. A curved arrow around the dashed line indicates a 180-degree rotation of the loop at constant angular speed omega. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831228-0LmgK6.jpg)

- **A.** \(0\)
- **B.** \(\dfrac{\omega N B_0 \pi r^2}{R}\)
- **C.** \(\dfrac{N B_0 \pi r^2}{R}\)
- **D.** \(\dfrac{2 N B_0 \pi r^2}{R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118706/*