A "long" solenoid of length 1.61 m has radius 7.24 cm, 6,303 turns and carries current 94.7. Now a small circular coil with 595 turns, radius 4.62 mm and carrying current 63.8 A is placed inside the coil so the planes of the two coils are at right angles to each other. Find the magnitude of the torque, in N-m, felt by the small coil.
A "long" solenoid of length 1.61 m has radius 7.24 cm, 6,303 turns and carries current 94.7. Now a small circular coil with 595 turns, radius 4.62 mm and carrying current 63.8 A is placed inside the coil so the planes of the two coils are at right angles to each other. Find the magnitude of the torque, in N-m, felt by the small coil.
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
Question in the attachment
![**Problem Statement:**
A "long" solenoid of length 1.61 m has a radius of 7.24 cm and 6,303 turns, carrying a current of 94.7 A. Now, a small circular coil with 595 turns, a radius of 4.62 mm, and carrying a current of 63.8 A is placed inside the solenoid. The planes of the two coils are at right angles to each other. Determine the magnitude of the torque, in N-m, experienced by the small coil.
**Solution Explanation:**
To solve this problem, use the following concepts:
1. **Magnetic Field Inside a Solenoid:**
The magnetic field \( B \) inside a long solenoid is given by:
\[
B = \mu_0 \cdot n \cdot I
\]
where \(\mu_0\) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}\)), \(n\) is the number of turns per unit length, and \(I\) is the current.
2. **Torque on a Coil in a Magnetic Field:**
The torque \(\tau\) on a current-carrying coil in a magnetic field is given by:
\[
\tau = n \cdot I \cdot A \cdot B \cdot \sin(\theta)
\]
where \(n\) is the number of turns, \(I\) is the current in the coil, \(A\) is the area of the coil, \(B\) is the magnetic field, and \(\theta\) is the angle between the magnetic field and the normal to the plane of the coil (\(90^\circ\) in this case, so \(\sin(\theta) = 1\)).
3. **Area of a Circular Coil:**
The area \(A\) of a circular coil with radius \(r\) is:
\[
A = \pi r^2
\]
Insert the given values and calculate the torque acting on the small coil.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbdfcc25e-a98a-4b3b-a24e-9aaac16ae47d%2F32ec7d2b-aba8-401a-9a5b-17833cb41999%2Ffkxtjt_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A "long" solenoid of length 1.61 m has a radius of 7.24 cm and 6,303 turns, carrying a current of 94.7 A. Now, a small circular coil with 595 turns, a radius of 4.62 mm, and carrying a current of 63.8 A is placed inside the solenoid. The planes of the two coils are at right angles to each other. Determine the magnitude of the torque, in N-m, experienced by the small coil.
**Solution Explanation:**
To solve this problem, use the following concepts:
1. **Magnetic Field Inside a Solenoid:**
The magnetic field \( B \) inside a long solenoid is given by:
\[
B = \mu_0 \cdot n \cdot I
\]
where \(\mu_0\) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}\)), \(n\) is the number of turns per unit length, and \(I\) is the current.
2. **Torque on a Coil in a Magnetic Field:**
The torque \(\tau\) on a current-carrying coil in a magnetic field is given by:
\[
\tau = n \cdot I \cdot A \cdot B \cdot \sin(\theta)
\]
where \(n\) is the number of turns, \(I\) is the current in the coil, \(A\) is the area of the coil, \(B\) is the magnetic field, and \(\theta\) is the angle between the magnetic field and the normal to the plane of the coil (\(90^\circ\) in this case, so \(\sin(\theta) = 1\)).
3. **Area of a Circular Coil:**
The area \(A\) of a circular coil with radius \(r\) is:
\[
A = \pi r^2
\]
Insert the given values and calculate the torque acting on the small coil.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 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