Two infinitely long solenoids (seen in cross section) pass through a circuit as shown in the figure on the right, with radii r = 0.150 m and r2 = 0.250 m and a = 0.500 m. The magnitude of the magnetic field in each solenoid is increasing in the direction shown at a rate of 40.0 T/s (into the page for solenoid on the left, out of the page for solenoid on the right). The magnetic field of the solenoid on the left is directed into the page, while the magnetic field of the solenoid on the right is directed out of the page. The three resistors have values R1 = 5.00 Q, R2 = 15.0 Q, and R3 = 12.0 Q. R1 R2 R3 Bin Bout a) What are the magnitudes of the emfs induced in each of the two loops of the circuit? b) What are the magnitudes and directions of the currents in each of the three resistors (specify upward or downward through each resistor)? It might be helpful to redraw the circuit with an appropriately oriented battery in the left loop and an appropriately oriented battery in the right loop.
Two infinitely long solenoids (seen in cross section) pass through a circuit as shown in the figure on the right, with radii r = 0.150 m and r2 = 0.250 m and a = 0.500 m. The magnitude of the magnetic field in each solenoid is increasing in the direction shown at a rate of 40.0 T/s (into the page for solenoid on the left, out of the page for solenoid on the right). The magnetic field of the solenoid on the left is directed into the page, while the magnetic field of the solenoid on the right is directed out of the page. The three resistors have values R1 = 5.00 Q, R2 = 15.0 Q, and R3 = 12.0 Q. R1 R2 R3 Bin Bout a) What are the magnitudes of the emfs induced in each of the two loops of the circuit? b) What are the magnitudes and directions of the currents in each of the three resistors (specify upward or downward through each resistor)? It might be helpful to redraw the circuit with an appropriately oriented battery in the left loop and an appropriately oriented battery in the right loop.
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
![## Circuit Analysis with Solenoids
### Problem Description
Two infinitely long solenoids pass through a circuit, shown in cross-section in the figure. Each solenoid has a specific radius and is aligned with radii \( r_1 = 0.150 \, \text{m} \) and \( r_2 = 0.250 \, \text{m} \), with separation \( a = 0.500 \, \text{m} \). The magnetic field in each solenoid is increasing at a rate of \( 40.0 \, \text{T/s} \).
- **Left Solenoid (in blue, \( B_{\text{in}} \)):** Magnetic field directed into the page.
- **Right Solenoid (in green, \( B_{\text{out}} \)):** Magnetic field directed out of the page.
The circuit includes three resistors:
- \( R_1 = 5.00 \, \Omega \)
- \( R_2 = 15.0 \, \Omega \)
- \( R_3 = 12.0 \, \Omega \)
### Diagram Explanation
The diagram shows:
- Two solenoids with magnetic fields indicated by circles with dots (field out of the page) and crosses (field into the page).
- A circuit with three resistors arranged around these solenoids.
### Questions
a) **What are the magnitudes of the emfs induced in each of the two loops of the circuit?**
b) **What are the magnitudes and directions of the currents in each of the three resistors (specify upward or downward through each resistor)?**
*Tip: Redraw the circuit with appropriately oriented batteries in each loop.*
### Solution Approach
To solve these questions, use Faraday's Law of Induction and Ohm's Law. Calculate the induced emf using:
\[
\text{emf} = -\frac{d\Phi_B}{dt}
\]
Where \(\Phi_B\) is the magnetic flux. Analyze each loop separately, considering contributions to the current through each resistor.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc102bb1-44c1-4032-a131-f496a2b2b6af%2F5abe116f-5248-4ae9-8c8d-bf0e9a1fd895%2Fpwpfx99_processed.png&w=3840&q=75)
Transcribed Image Text:## Circuit Analysis with Solenoids
### Problem Description
Two infinitely long solenoids pass through a circuit, shown in cross-section in the figure. Each solenoid has a specific radius and is aligned with radii \( r_1 = 0.150 \, \text{m} \) and \( r_2 = 0.250 \, \text{m} \), with separation \( a = 0.500 \, \text{m} \). The magnetic field in each solenoid is increasing at a rate of \( 40.0 \, \text{T/s} \).
- **Left Solenoid (in blue, \( B_{\text{in}} \)):** Magnetic field directed into the page.
- **Right Solenoid (in green, \( B_{\text{out}} \)):** Magnetic field directed out of the page.
The circuit includes three resistors:
- \( R_1 = 5.00 \, \Omega \)
- \( R_2 = 15.0 \, \Omega \)
- \( R_3 = 12.0 \, \Omega \)
### Diagram Explanation
The diagram shows:
- Two solenoids with magnetic fields indicated by circles with dots (field out of the page) and crosses (field into the page).
- A circuit with three resistors arranged around these solenoids.
### Questions
a) **What are the magnitudes of the emfs induced in each of the two loops of the circuit?**
b) **What are the magnitudes and directions of the currents in each of the three resistors (specify upward or downward through each resistor)?**
*Tip: Redraw the circuit with appropriately oriented batteries in each loop.*
### Solution Approach
To solve these questions, use Faraday's Law of Induction and Ohm's Law. Calculate the induced emf using:
\[
\text{emf} = -\frac{d\Phi_B}{dt}
\]
Where \(\Phi_B\) is the magnetic flux. Analyze each loop separately, considering contributions to the current through each resistor.
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 3 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