Consider two magnetic fields B1 and B2, with components B1x = 0, B1y = 2ax, and B1z = 0 and B2x = -ay, B2y = ax, and B2z = 0, respectively, where a is a constant. a. Draw a picture of each field. (Hint: Show that the second field points circularly around the origin. How does its magnitude depend on the distance from the origin?) b. Show that these fields have the same curl everywhere. c. Consider the following statement: "If we know a magnetic field's curl at all points, we can determine the magnetic field at all points." In light of what you have discovered above, why is this statement false?
Consider two magnetic fields B1 and B2, with components B1x = 0, B1y = 2ax, and B1z = 0 and B2x = -ay, B2y = ax, and B2z = 0, respectively, where a is a constant. a. Draw a picture of each field. (Hint: Show that the second field points circularly around the origin. How does its magnitude depend on the distance from the origin?) b. Show that these fields have the same curl everywhere. c. Consider the following statement: "If we know a magnetic field's curl at all points, we can determine the magnetic field at all points." In light of what you have discovered above, why is this statement false?
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter30: Magnetic Fields And Forces
Section: Chapter Questions
Problem 48PQ
Related questions
Question
Consider two magnetic fields B1 and B2, with components B1x = 0, B1y = 2ax, and B1z = 0 and B2x = -ay, B2y = ax, and B2z = 0, respectively, where a is a constant.
a. Draw a picture of each field. (Hint: Show that the second field points circularly around the origin. How does its magnitude depend on the distance from the origin?)
b. Show that these fields have the same curl everywhere.
c. Consider the following statement: "If we know a magnetic field's curl at all points, we can determine the magnetic field at all points." In light of what you have discovered above, why is this statement false?
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 1 steps with 2 images
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
Glencoe Physics: Principles and Problems, Student…
Physics
ISBN:
9780078807213
Author:
Paul W. Zitzewitz
Publisher:
Glencoe/McGraw-Hill
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
Glencoe Physics: Principles and Problems, Student…
Physics
ISBN:
9780078807213
Author:
Paul W. Zitzewitz
Publisher:
Glencoe/McGraw-Hill
College Physics
Physics
ISBN:
9781938168000
Author:
Paul Peter Urone, Roger Hinrichs
Publisher:
OpenStax College
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
College Physics
Physics
ISBN:
9781285737027
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning