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?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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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?
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