---
title: "Two parallel, frictionless conducting rails separated by a distance \\(d\\) are tilted at an angle \\(\\theta\\) above the horizontal. A uniform magnetic field of magnitude \\(B\\) is directed vertically upward throughout the region. A conducting rod of mass \\(m\\) and length \\(d\\) rests across the rails, perpendicular to the incline, and carries a constant externally supplied current \\(I\\) such that the magnetic force pushes the rod up the incline. Assuming the acceleration due to gravity is \\(g\\), what is the magnitude of the acceleration of the rod up the incline?"
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/121255/"
date_modified: "2026-08-23T04:59:02+00:00"
---

# Two parallel, frictionless conducting rails separated by a distance \(d\) are tilted at an angle \(\theta\) above the horizontal. A uniform magnetic field of magnitude \(B\) is directed vertically upward throughout the region. A conducting rod of mass \(m\) and length \(d\) rests across the rails, perpendicular to the incline, and carries a constant externally supplied current \(I\) such that the magnetic force pushes the rod up the incline. Assuming the acceleration due to gravity is \(g\), what is the magnitude of the acceleration of the rod up the incline?

Two parallel, frictionless conducting rails separated by a distance \(d\) are tilted at an angle \(\theta\) above the horizontal. A uniform magnetic field of magnitude \(B\) is directed vertically upward throughout the region. A conducting rod of mass \(m\) and length \(d\) rests across the rails, perpendicular to the incline, and carries a constant externally supplied current \(I\) such that the magnetic force pushes the rod up the incline. Assuming the acceleration due to gravity is \(g\), what is the magnitude of the acceleration of the rod up the incline?

![A side-view and perspective schematic of a physical setup. A wedge-shaped inclined plane makes an angle \(\theta\) with the horizontal base. Two parallel, straight conducting rails are fixed along the inclined surface, separated by a distance \(d\). A straight cylindrical conducting rod of mass \(m\) and length \(d\) rests horizontally across both rails, oriented perpendicular to the slope. A curved arrow along the rod indicates current \(I\). Exactly three identical, vertical, upward-pointing arrows labeled \(\vec{B}\) represent a uniform magnetic field throughout the region. An angle arc at the bottom-left corner of the incline is labeled \(\theta\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461141-xmgPib.jpg)

- **A.** \(\dfrac{I d B \cos\theta}{m} - g \sin\theta\)
- **B.** \(\dfrac{I d B \sin\theta}{m} - g \sin\theta\)
- **C.** \(\dfrac{I d B}{m} - g \sin\theta\)
- **D.** \(\dfrac{I d B \cos\theta}{m} + g \sin\theta\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121255/*