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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![### Magnetic Force on a Current-Carrying Wire
**Problem Statement:**
A wire with current \(I = 0.9\, \text{A}\) in the \(x\)-\(y\) plane is placed in a magnetic field \(B = 0.5\, \text{T}\) as shown in the figure. Find the value of the net magnetic force on the wire (in Newtons).
**Details of the Diagram:**
In the provided diagram:
- The \(B\)-field (magnetic field) is oriented into the plane of the paper, indicated by crosses.
- The wire is arranged in an angular shape within the \(x\)-\(y\) plane.
- The wire segments form a structure where it is divided into various lengths and angles.
- Notable lengths and positions include:
- The bottom segment is horizontally 4 meters long.
- The vertical height is 4 meters in total, starting from 0 up to 4 meters in the y-axis.
- Along the x-axis, the wire segments have horizontal components of (from left to right) 3 meters and 1 meter, and a height component that forms the angular connections inside the rectangular arrangement.
**Mathematics:**
The force \( \mathbf{F} \) on a current-carrying wire in a magnetic field is given by:
\[ \mathbf{F} = I (\mathbf{L} \times \mathbf{B}) \]
Where:
- \(I\) is the current
- \(\mathbf{L}\) is the length vector of the wire segment
- \(\mathbf{B}\) is the magnetic field vector
Since \(\mathbf{B}\) is into the paper, \(\mathbf{B} = B \hat{z}\), and the force on each wire segment must be calculated using the right-hand rule and summing vectorially.
**Answer Choices:**
1. \(0.90\, \text{N}\)
2. \(1.05\, \text{N}\)
3. \(1.20\, \text{N}\)
4. \(1.35\, \text{N}\)
5. \(1.50\, \text{N}\)
This problem requires the use of vector calculus to determine the forces on different segments of the wire based on the given magnetic field strength and arrangement.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbeae604a-2e4b-47ef-907a-313aaf16b611%2F48718d3b-4ad6-4704-a0a8-6fe2078a1e1f%2Fiucnvs8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Magnetic Force on a Current-Carrying Wire
**Problem Statement:**
A wire with current \(I = 0.9\, \text{A}\) in the \(x\)-\(y\) plane is placed in a magnetic field \(B = 0.5\, \text{T}\) as shown in the figure. Find the value of the net magnetic force on the wire (in Newtons).
**Details of the Diagram:**
In the provided diagram:
- The \(B\)-field (magnetic field) is oriented into the plane of the paper, indicated by crosses.
- The wire is arranged in an angular shape within the \(x\)-\(y\) plane.
- The wire segments form a structure where it is divided into various lengths and angles.
- Notable lengths and positions include:
- The bottom segment is horizontally 4 meters long.
- The vertical height is 4 meters in total, starting from 0 up to 4 meters in the y-axis.
- Along the x-axis, the wire segments have horizontal components of (from left to right) 3 meters and 1 meter, and a height component that forms the angular connections inside the rectangular arrangement.
**Mathematics:**
The force \( \mathbf{F} \) on a current-carrying wire in a magnetic field is given by:
\[ \mathbf{F} = I (\mathbf{L} \times \mathbf{B}) \]
Where:
- \(I\) is the current
- \(\mathbf{L}\) is the length vector of the wire segment
- \(\mathbf{B}\) is the magnetic field vector
Since \(\mathbf{B}\) is into the paper, \(\mathbf{B} = B \hat{z}\), and the force on each wire segment must be calculated using the right-hand rule and summing vectorially.
**Answer Choices:**
1. \(0.90\, \text{N}\)
2. \(1.05\, \text{N}\)
3. \(1.20\, \text{N}\)
4. \(1.35\, \text{N}\)
5. \(1.50\, \text{N}\)
This problem requires the use of vector calculus to determine the forces on different segments of the wire based on the given magnetic field strength and arrangement.
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