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Evaluate the magnitude of the net magnetic force on a current loop of 1₁ = 9R, l₂ = 4.6R, and r = 6R in an external magnetic field B = 3.2B₂(−î) in terms of BØRI. Express your answer using two decimal places. Please note that a current of 41 runs on the wire. 4₂ O e B 41 4₁ •

Evaluate the magnitude of the net magnetic force on a current loop of 1₁ = 9R, l₂ = 4.6R, and r = 6R in an external magnetic field B = 3.2B₂(−î) in terms of BØRI. Express your answer using two decimal places. Please note that a current of 41 runs on the wire. 4₂ O e B 41 4₁ •

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Evaluating the Magnitude of Net Magnetic Force on a Current Loop **Problem Statement:** Evaluate the magnitude of the net magnetic force on a current loop with the following parameters: - \( l_1 = 9R \) - \( l_2 = 4.6R \) - \( r = 6R \) The loop is placed in an external magnetic field \( \vec{B} = 3.2B_0(-\hat{i}) \). Express your answer in terms of \( B_0, R, \) and \( I\), using two decimal places. Note that a current of \( 4I \) runs through the wire. **Diagram Explanation:** The provided diagram depicts the current loop and the orientation of the magnetic field. Here is a detailed explanation of the components: 1. **Coordinate Axes:** The directions are indicated with \( x \), \( y \), and \( z \) axes. 2. **Magnetic Field (\( \vec{B} \)):** Represented by parallel yellow lines pointing to the left (negative \( x \)-direction). This shows the uniform magnetic field \( \vec{B} = 3.2B_0(-\hat{i}) \). 3. **Current Loop:** The current loop has the following measurements: - \( l_1 \) is a horizontal component of length \( 9R \) on the bottom. - \( l_2 \) is a vertical component of length \( 4.6R \). - A semicircular arc of radius \( 6R \) connects the endpoints of \( l_1 \) and \( l_2 \). - The point \( O \) is the origin where calculations start. 4. **Current (4I):** The electric current \( 4I \) flows through the loop. The direction of current flow is indicated by arrows on the diagram. 5. **Angle \( \theta \):** Denotes the angle in the semicircular arc. ### Solution Steps: To solve for the magnitude of the net magnetic force: 1. **Evaluate the Magnetic Force Components:** Use the formula \( \vec{F} = I (\vec{L} \times \vec{B}) \), where \( \vec{F} \) is the magnetic force, \( I \) is the current, \( \vec{L} \
Transcribed Image Text:### Evaluating the Magnitude of Net Magnetic Force on a Current Loop **Problem Statement:** Evaluate the magnitude of the net magnetic force on a current loop with the following parameters: - \( l_1 = 9R \) - \( l_2 = 4.6R \) - \( r = 6R \) The loop is placed in an external magnetic field \( \vec{B} = 3.2B_0(-\hat{i}) \). Express your answer in terms of \( B_0, R, \) and \( I\), using two decimal places. Note that a current of \( 4I \) runs through the wire. **Diagram Explanation:** The provided diagram depicts the current loop and the orientation of the magnetic field. Here is a detailed explanation of the components: 1. **Coordinate Axes:** The directions are indicated with \( x \), \( y \), and \( z \) axes. 2. **Magnetic Field (\( \vec{B} \)):** Represented by parallel yellow lines pointing to the left (negative \( x \)-direction). This shows the uniform magnetic field \( \vec{B} = 3.2B_0(-\hat{i}) \). 3. **Current Loop:** The current loop has the following measurements: - \( l_1 \) is a horizontal component of length \( 9R \) on the bottom. - \( l_2 \) is a vertical component of length \( 4.6R \). - A semicircular arc of radius \( 6R \) connects the endpoints of \( l_1 \) and \( l_2 \). - The point \( O \) is the origin where calculations start. 4. **Current (4I):** The electric current \( 4I \) flows through the loop. The direction of current flow is indicated by arrows on the diagram. 5. **Angle \( \theta \):** Denotes the angle in the semicircular arc. ### Solution Steps: To solve for the magnitude of the net magnetic force: 1. **Evaluate the Magnetic Force Components:** Use the formula \( \vec{F} = I (\vec{L} \times \vec{B}) \), where \( \vec{F} \) is the magnetic force, \( I \) is the current, \( \vec{L} \
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