---
title: "A conducting rod of mass \\(m\\) and negligible electrical resistance is free to slide along a pair of horizontal, frictionless, parallel conducting rails separated by a distance \\(\\ell\\). The rails are connected at one end by a fixed resistor of resistance \\(R\\), and a uniform magnetic field of magnitude \\(B\\) is directed perpendicular to the plane of the rails. At time \\(t = 0\\), the rod is moving away from the resistor with speed \\(v_0\\) while a constant external force of magnitude \\(F_0\\) is applied to the rod in the direction of its motion, where \\(F_0 < \\dfrac{B^2 \\ell^2 v_0}{R}\\). Which of the following best describes the shape of the rod's velocity \\(v\\) as a function of time \\(t\\) for \\(t \\ge 0\\)?"
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url: "https://nerd-notes.com/ubq/121325/"
date_modified: "2026-08-23T04:59:44+00:00"
---

# A conducting rod of mass \(m\) and negligible electrical resistance is free to slide along a pair of horizontal, frictionless, parallel conducting rails separated by a distance \(\ell\). The rails are connected at one end by a fixed resistor of resistance \(R\), and a uniform magnetic field of magnitude \(B\) is directed perpendicular to the plane of the rails. At time \(t = 0\), the rod is moving away from the resistor with speed \(v_0\) while a constant external force of magnitude \(F_0\) is applied to the rod in the direction of its motion, where \(F_0 < \dfrac{B^2 \ell^2 v_0}{R}\). Which of the following best describes the shape of the rod's velocity \(v\) as a function of time \(t\) for \(t \ge 0\)?

A conducting rod of mass \(m\) and negligible electrical resistance is free to slide along a pair of horizontal, frictionless, parallel conducting rails separated by a distance \(\ell\). The rails are connected at one end by a fixed resistor of resistance \(R\), and a uniform magnetic field of magnitude \(B\) is directed perpendicular to the plane of the rails. At time \(t = 0\), the rod is moving away from the resistor with speed \(v_0\) while a constant external force of magnitude \(F_0\) is applied to the rod in the direction of its motion, where \(F_0 < \dfrac{B^2 \ell^2 v_0}{R}\). Which of the following best describes the shape of the rod's velocity \(v\) as a function of time \(t\) for \(t \ge 0\)?

![A top-down schematic view of two horizontal parallel lines representing conducting rails. At the left end, a vertical zigzag resistor symbol connects the two rails and is labeled R. A vertical solid bar spanning the distance between the rails represents a conducting rod labeled m. A horizontal solid arrow labeled \vec{F}_0 points to the right from the center of the rod, and a horizontal dashed arrow labeled \vec{v}_0 points to the right above the rod. A uniform grid of six cross symbols indicating an into-the-page magnetic field is distributed between the rails, accompanied by a label \vec{B} in the upper region. A vertical double-headed dimension arrow indicates the rail separation labeled \ell. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461183-O6IotN.jpg)

- **A.** Starts at \(v_0\), increases with concave-down curvature, and asymptotically approaches a terminal velocity greater than \(v_0\)
- **B.** Starts at \(v_0\) and decreases linearly with a constant negative slope until reaching zero at a finite time
- **C.** Starts at \(v_0\), decreases with concave-up curvature, and asymptotically approaches a non-zero positive terminal velocity
- **D.** Starts at \(v_0\), decreases with concave-up curvature, and asymptotically approaches zero

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121325/*