A coaxial cable consists of a long cylindrical wire (black) of radius a carrying current I in the +z direction, surrounded by a hollow cylindrical conductor (red) of inner radius b and outer radius c, where c> b> a. The outer conductor carries current I in the -z direction, that is, the same current as the inner conductor but in the opposite direction. In both conductors, the current is distributed uniformly over the cross-sectional area. Use Ampere's law to find the magnetic field at all points in this current configuration. Each path you draw should be a circle of constant radius. (a) Find the magnetic field inside the inner conductor, i.e. at a distance r from the cable center where r c.
A coaxial cable consists of a long cylindrical wire (black) of radius a carrying current I in the +z direction, surrounded by a hollow cylindrical conductor (red) of inner radius b and outer radius c, where c> b> a. The outer conductor carries current I in the -z direction, that is, the same current as the inner conductor but in the opposite direction. In both conductors, the current is distributed uniformly over the cross-sectional area. Use Ampere's law to find the magnetic field at all points in this current configuration. Each path you draw should be a circle of constant radius. (a) Find the magnetic field inside the inner conductor, i.e. at a distance r from the cable center where r c.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![A coaxial cable consists of a long cylindrical wire (black) of radius a carrying current I in the +z direction, surrounded by a hollow cylindrical conductor (red) of inner radius b and outer radius c, where c > b > a. The outer conductor carries current I in the -z direction, that is, the
same current as the inner conductor but in the opposite direction. In both conductors, the current is distributed uniformly over the cross-sectional area.
a
b
Use Ampere's law to find the magnetic field at all points in this current configuration. Each path you draw should be a circle of constant radius.
(a) Find the magnetic field inside the inner conductor, i.e. at a distancer from the cable center where r < a.
(b) Find the magnetic field for a < r < b in the space between the conductors.
(c) Find the magnetic field inside the outer conductor, i.e. where b < r < c.
Hint: this was one of the Test 2 Review problems. Of course, you need to derive the answer yourself.
(d) Find the magnetic field outside the cable, for r > c.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73d5c005-90a3-445f-a212-af9c00b9cb08%2F6a764c6c-a875-42a0-8208-eef4fac6c0a8%2Fo2m8yjl_processed.png&w=3840&q=75)
Transcribed Image Text:A coaxial cable consists of a long cylindrical wire (black) of radius a carrying current I in the +z direction, surrounded by a hollow cylindrical conductor (red) of inner radius b and outer radius c, where c > b > a. The outer conductor carries current I in the -z direction, that is, the
same current as the inner conductor but in the opposite direction. In both conductors, the current is distributed uniformly over the cross-sectional area.
a
b
Use Ampere's law to find the magnetic field at all points in this current configuration. Each path you draw should be a circle of constant radius.
(a) Find the magnetic field inside the inner conductor, i.e. at a distancer from the cable center where r < a.
(b) Find the magnetic field for a < r < b in the space between the conductors.
(c) Find the magnetic field inside the outer conductor, i.e. where b < r < c.
Hint: this was one of the Test 2 Review problems. Of course, you need to derive the answer yourself.
(d) Find the magnetic field outside the cable, for r > c.
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