A loop of wire is at the edge of a region of space containing a uniform magnetic field B⃗. The plane of the loop is perpendicular to the magnetic field. Now the loop is pulled out of this region in such a way that the area Aof the coil inside the magnetic field region is decreasing at the constant rate ccc. That is, dA/dt=−c, with c>0. For the case of a square loop of side length L being pulled out of the magnetic field with constant speed v (see the figure), what is the rate of change of area c=−dA/dt?
A loop of wire is at the edge of a region of space containing a uniform magnetic field B⃗. The plane of the loop is perpendicular to the magnetic field. Now the loop is pulled out of this region in such a way that the area Aof the coil inside the magnetic field region is decreasing at the constant rate ccc. That is, dA/dt=−c, with c>0. For the case of a square loop of side length L being pulled out of the magnetic field with constant speed v (see the figure), what is the rate of change of area c=−dA/dt?
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
A loop of wire is at the edge of a region of space containing a uniform magnetic field B⃗. The plane of the loop is perpendicular to the magnetic field. Now the loop is pulled out of this region in such a way that the area Aof the coil inside the magnetic field region is decreasing at the constant rate ccc. That is, dA/dt=−c, with c>0. For the case of a square loop of side length L being pulled out of the magnetic field with constant speed v (see the figure), what is the rate of change of area c=−dA/dt?
![**Transcription for Educational Website**
---
### Understanding Magnetic Induction in a Loop of Wire
**Concept Overview:**
A loop of wire is positioned at the boundary of a spatial region containing a uniform magnetic field, denoted as \(\vec{B}\). The loop's plane is orthogonal to the magnetic field. When the loop is gradually pulled from this region, the area \(A\) of the coil that remains within the magnetic field diminishes at a constant rate \(c\). Mathematically, this is expressed as:
\[
\frac{dA}{dt} = -C, \quad \text{where } C > 0.
\]
**Part B: Rate of Change of Area**
For a square loop with side length \(L\) being extracted from the magnetic field at a uniform speed \(v\) (see accompanying figure), the task is to determine the rate of change of area \(C\), given by \(-\frac{dA}{dt}\).
**Express your answer in terms of \(L\) and \(v\).**
Here's the equation provided by the user:
\[
C = \frac{L^2}{v}
\]
*Note: This submission is currently incorrect, and recalculations may be necessary. Attempts remaining: 2.*
**Figure Explanation:**
The figure illustrates a square loop within a magnetic field indicated by a grid of "X" symbols, which denotes the field directed into the plane. The loop's side is marked as \(L\), and it's being pulled to the right at a constant speed \(v\).
---
For further inquiry or discussion, feedback can be provided through the respective section.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd75a0cba-20f2-443d-a1e9-f3f1ac2380ac%2F67902000-689b-4ca5-8ea7-7312c406b00e%2Fojgcmbv_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
---
### Understanding Magnetic Induction in a Loop of Wire
**Concept Overview:**
A loop of wire is positioned at the boundary of a spatial region containing a uniform magnetic field, denoted as \(\vec{B}\). The loop's plane is orthogonal to the magnetic field. When the loop is gradually pulled from this region, the area \(A\) of the coil that remains within the magnetic field diminishes at a constant rate \(c\). Mathematically, this is expressed as:
\[
\frac{dA}{dt} = -C, \quad \text{where } C > 0.
\]
**Part B: Rate of Change of Area**
For a square loop with side length \(L\) being extracted from the magnetic field at a uniform speed \(v\) (see accompanying figure), the task is to determine the rate of change of area \(C\), given by \(-\frac{dA}{dt}\).
**Express your answer in terms of \(L\) and \(v\).**
Here's the equation provided by the user:
\[
C = \frac{L^2}{v}
\]
*Note: This submission is currently incorrect, and recalculations may be necessary. Attempts remaining: 2.*
**Figure Explanation:**
The figure illustrates a square loop within a magnetic field indicated by a grid of "X" symbols, which denotes the field directed into the plane. The loop's side is marked as \(L\), and it's being pulled to the right at a constant speed \(v\).
---
For further inquiry or discussion, feedback can be provided through the respective section.
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 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