A flat, 102 turn current-carrying loop is immersed in a uniform magnetic field. The area of the loop is 4.25 x 10-4 m², and the angle between its magnetic dipole moment and the field is 40.9°. Find the strength B of the magnetic field that causes a torque of 1.29 x 10-5 N-m to act on the loop when a current of 0.00311 A flows in it. B = T
A flat, 102 turn current-carrying loop is immersed in a uniform magnetic field. The area of the loop is 4.25 x 10-4 m², and the angle between its magnetic dipole moment and the field is 40.9°. Find the strength B of the magnetic field that causes a torque of 1.29 x 10-5 N-m to act on the loop when a current of 0.00311 A flows in it. B = T
Principles of Physics: A Calculus-Based Text
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ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter22: Magnetic Forces And Magnetic Fields
Section: Chapter Questions
Problem 33P: One long wire carries current 30.0 A to the left along the x axis. A second long wire carries...
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![### Problem Description:
A flat, 102 turn current-carrying loop is immersed in a uniform magnetic field. The area of the loop is \(4.25 \times 10^{-4} \text{ m}^2\), and the angle between its magnetic dipole moment and the field is \(40.9^\circ\). Find the strength \(B\) of the magnetic field that causes a torque of \(1.29 \times 10^{-5} \text{ N·m}\) to act on the loop when a current of \(0.00311 \text{ A}\) flows in it.
### Given Data:
- Number of turns, \(N = 102\)
- Area of the loop, \(A = 4.25 \times 10^{-4} \text{ m}^2\)
- Angle between magnetic dipole moment and field, \(\theta = 40.9^\circ\)
- Torque, \(\tau = 1.29 \times 10^{-5} \text{ N·m}\)
- Current, \(I = 0.00311 \text{ A}\)
### Formula to Use:
The torque \(\tau\) experienced by a current-carrying loop in a magnetic field is given by:
\[
\tau = N \cdot I \cdot A \cdot B \cdot \sin(\theta)
\]
Where:
- \(\tau\) is the torque
- \(N\) is the number of turns
- \(I\) is the current
- \(A\) is the area of the loop
- \(B\) is the magnetic field strength
- \(\theta\) is the angle between the magnetic dipole moment and the magnetic field
### Calculate Magnetic Field Strength \(B\):
Isolate \(B\) in the equation:
\[
B = \frac{\tau}{N \cdot I \cdot A \cdot \sin(\theta)}
\]
Substitute the given values:
\[
B = \frac{1.29 \times 10^{-5} \text{ N·m}}{102 \cdot 0.00311 \text{ A} \cdot 4.25 \times 10^{-4} \text{ m}^2 \cdot \sin(40.9^\circ)}
\]
Calculate \(\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37e1db01-06d0-4e20-aae1-26f96b6814c3%2Ff3c3b6d2-0df7-4148-9db6-a66d188d1330%2F9ce9h5l_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description:
A flat, 102 turn current-carrying loop is immersed in a uniform magnetic field. The area of the loop is \(4.25 \times 10^{-4} \text{ m}^2\), and the angle between its magnetic dipole moment and the field is \(40.9^\circ\). Find the strength \(B\) of the magnetic field that causes a torque of \(1.29 \times 10^{-5} \text{ N·m}\) to act on the loop when a current of \(0.00311 \text{ A}\) flows in it.
### Given Data:
- Number of turns, \(N = 102\)
- Area of the loop, \(A = 4.25 \times 10^{-4} \text{ m}^2\)
- Angle between magnetic dipole moment and field, \(\theta = 40.9^\circ\)
- Torque, \(\tau = 1.29 \times 10^{-5} \text{ N·m}\)
- Current, \(I = 0.00311 \text{ A}\)
### Formula to Use:
The torque \(\tau\) experienced by a current-carrying loop in a magnetic field is given by:
\[
\tau = N \cdot I \cdot A \cdot B \cdot \sin(\theta)
\]
Where:
- \(\tau\) is the torque
- \(N\) is the number of turns
- \(I\) is the current
- \(A\) is the area of the loop
- \(B\) is the magnetic field strength
- \(\theta\) is the angle between the magnetic dipole moment and the magnetic field
### Calculate Magnetic Field Strength \(B\):
Isolate \(B\) in the equation:
\[
B = \frac{\tau}{N \cdot I \cdot A \cdot \sin(\theta)}
\]
Substitute the given values:
\[
B = \frac{1.29 \times 10^{-5} \text{ N·m}}{102 \cdot 0.00311 \text{ A} \cdot 4.25 \times 10^{-4} \text{ m}^2 \cdot \sin(40.9^\circ)}
\]
Calculate \(\
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