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
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)...
Related questions
Question
100%
what is the answer??! help!
![### 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 \(\
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON