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title: "A horizontal conducting bar of length \\(\\ell\\) and mass \\(m\\) slides vertically downward without friction along two parallel vertical conducting rails separated by distance \\(\\ell\\). The top ends of the rails are connected by a resistor of resistance \\(R\\), and a uniform magnetic field of magnitude \\(B\\) is directed perpendicular to the plane of the rails. The bar is released from rest and reaches a terminal speed \\(v_T\\) under the influence of gravity. Consider the following four configurations:  – Configuration 1: Mass \\(m\\), resistance \\(R\\), magnetic field \\(B\\) – Configuration 2: Mass \\(2m\\), resistance \\(R\\), magnetic field \\(B\\) – Configuration 3: Mass \\(m\\), resistance \\(2R\\), magnetic field \\(B\\) – Configuration 4: Mass \\(m\\), resistance \\(R\\), magnetic field \\(2B\\)  Which of the following correctly ranks the terminal speed \\(v_T\\) of the bar in each configuration?"
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url: "https://nerd-notes.com/ubq/118655/"
date_modified: "2026-08-04T08:13:31+00:00"
---

# A horizontal conducting bar of length \(\ell\) and mass \(m\) slides vertically downward without friction along two parallel vertical conducting rails separated by distance \(\ell\). The top ends of the rails are connected by a resistor of resistance \(R\), and a uniform magnetic field of magnitude \(B\) is directed perpendicular to the plane of the rails. The bar is released from rest and reaches a terminal speed \(v_T\) under the influence of gravity. Consider the following four configurations:

– Configuration 1: Mass \(m\), resistance \(R\), magnetic field \(B\)
– Configuration 2: Mass \(2m\), resistance \(R\), magnetic field \(B\)
– Configuration 3: Mass \(m\), resistance \(2R\), magnetic field \(B\)
– Configuration 4: Mass \(m\), resistance \(R\), magnetic field \(2B\)

Which of the following correctly ranks the terminal speed \(v_T\) of the bar in each configuration?

A horizontal conducting bar of length \(\ell\) and mass \(m\) slides vertically downward without friction along two parallel vertical conducting rails separated by distance \(\ell\). The top ends of the rails are connected by a resistor of resistance \(R\), and a uniform magnetic field of magnitude \(B\) is directed perpendicular to the plane of the rails. The bar is released from rest and reaches a terminal speed \(v_T\) under the influence of gravity. Consider the following four configurations:

- Configuration 1: Mass \(m\), resistance \(R\), magnetic field \(B\)
- Configuration 2: Mass \(2m\), resistance \(R\), magnetic field \(B\)
- Configuration 3: Mass \(m\), resistance \(2R\), magnetic field \(B\)
- Configuration 4: Mass \(m\), resistance \(R\), magnetic field \(2B\)

Which of the following correctly ranks the terminal speed \(v_T\) of the bar in each configuration?

![A schematic showing two vertical parallel conducting rails connected at the top by a resistor labeled R. A horizontal conducting bar of length l and mass m spans between the rails. A uniform magnetic field pointing into the page is represented by a grid of small crosses labeled B. An arrow pointing downward from the center of the bar represents the force of gravity mg.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831211-fLvBx1.jpg)

- **A.** \(v_4 > v_1 > (v_2 = v_3)\)
- **B.** \((v_2 = v_3) > v_1 > v_4\)
- **C.** \(v_2 > v_3 > v_1 > v_4\)
- **D.** \((v_2 = v_3) > v_4 > v_1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118655/*