7. A conducting rod whose length is e= 1.60 m is placed on frictionless U-shaped metal rails that is connected to a lightbulb having a resistance of 4.00 2 as shown in the figure. A constant uniform magnetic field of strength 2.20 T is applied perpendicular to and out of the paper. What is the magnitude of the external applied force needed to move the rod to the right with a constant speed of 6.00 m/s?

College Physics
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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**Problem 7: Magnetic Force on a Conducting Rod**

A conducting rod with a length of \( \ell = 1.60 \, \text{m} \) is placed on frictionless U-shaped metal rails. This rod is connected to a light bulb with a resistance of \( 4.00 \, \Omega \), as depicted in the figure. A constant uniform magnetic field with a strength of \( 2.20 \, \text{T} \) is applied perpendicular to the paper and directed outwards. Determine the magnitude of the external force required to move the rod to the right at a constant speed of \( 6.00 \, \text{m/s} \).

**Diagram Explanation:**

The diagram shows a rectangular setup with the conducting rod on top of the rails, represented as a vertical line. The magnetic field is illustrated by dots, indicating it is directed out of the page. The rod is labeled with its length \( \ell \), and a note below indicates the magnetic field direction: "B-field \( \perp \) out (\( \cdot \))".

**Key Elements:**

- Conducting Rod Length: \( \ell = 1.60 \, \text{m} \)
- Resistance of Lightbulb: \( 4.00 \, \Omega \)
- Magnetic Field Strength: \( 2.20 \, \text{T} \)
- Desired Speed: \( 6.00 \, \text{m/s} \) 

Determine the required force to maintain the rod's motion at the given constant speed.
Transcribed Image Text:**Problem 7: Magnetic Force on a Conducting Rod** A conducting rod with a length of \( \ell = 1.60 \, \text{m} \) is placed on frictionless U-shaped metal rails. This rod is connected to a light bulb with a resistance of \( 4.00 \, \Omega \), as depicted in the figure. A constant uniform magnetic field with a strength of \( 2.20 \, \text{T} \) is applied perpendicular to the paper and directed outwards. Determine the magnitude of the external force required to move the rod to the right at a constant speed of \( 6.00 \, \text{m/s} \). **Diagram Explanation:** The diagram shows a rectangular setup with the conducting rod on top of the rails, represented as a vertical line. The magnetic field is illustrated by dots, indicating it is directed out of the page. The rod is labeled with its length \( \ell \), and a note below indicates the magnetic field direction: "B-field \( \perp \) out (\( \cdot \))". **Key Elements:** - Conducting Rod Length: \( \ell = 1.60 \, \text{m} \) - Resistance of Lightbulb: \( 4.00 \, \Omega \) - Magnetic Field Strength: \( 2.20 \, \text{T} \) - Desired Speed: \( 6.00 \, \text{m/s} \) Determine the required force to maintain the rod's motion at the given constant speed.
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