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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. 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)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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### Understanding the Magnetic Field in a Coaxial Cable A coaxial cable consists of a long cylindrical wire (black) of radius \(a\) carrying current \(I\) in the \(+z\) direction. It is surrounded by a hollow cylindrical conductor (red) with an inner radius \(b\) and outer radius \(c\), where \(c > b > a\). The outer conductor carries current \(I\) in the \(-z\) direction, meaning the same current flows in the inner conductor but in the opposite direction. In both conductors, the current is uniformly distributed over the cross-sectional area. #### Diagram Explanation The diagram shows a cross-section of the coaxial cable, illustrating: - A black central circle representing the inner cylindrical wire with radius \(a\). - A surrounding red ring representing the outer conductor with inner radius \(b\) and outer radius \(c\). #### Problem Statement Use Ampere's law to determine the magnetic field at all points within this configuration. Each path drawn should be a circle of constant radius. **Tasks:** (a) **Inside the Inner Conductor**: Find the magnetic field at a distance \(r\) from the cable center where \(r < a\). (b) **Between the Conductors**: Determine the magnetic field for \(a < r < b\), in the space between the conductors. (c) **Inside the Outer Conductor**: Calculate the magnetic field, i.e., where \(b < r < c\). - *Hint*: This was one of the [Test 2 Review problems.](#). Remember, derive the answer independently. (d) **Outside the Cable**: Find the magnetic field where \(r > c\).
Transcribed Image Text:### Understanding the Magnetic Field in a Coaxial Cable A coaxial cable consists of a long cylindrical wire (black) of radius \(a\) carrying current \(I\) in the \(+z\) direction. It is surrounded by a hollow cylindrical conductor (red) with an inner radius \(b\) and outer radius \(c\), where \(c > b > a\). The outer conductor carries current \(I\) in the \(-z\) direction, meaning the same current flows in the inner conductor but in the opposite direction. In both conductors, the current is uniformly distributed over the cross-sectional area. #### Diagram Explanation The diagram shows a cross-section of the coaxial cable, illustrating: - A black central circle representing the inner cylindrical wire with radius \(a\). - A surrounding red ring representing the outer conductor with inner radius \(b\) and outer radius \(c\). #### Problem Statement Use Ampere's law to determine the magnetic field at all points within this configuration. Each path drawn should be a circle of constant radius. **Tasks:** (a) **Inside the Inner Conductor**: Find the magnetic field at a distance \(r\) from the cable center where \(r < a\). (b) **Between the Conductors**: Determine the magnetic field for \(a < r < b\), in the space between the conductors. (c) **Inside the Outer Conductor**: Calculate the magnetic field, i.e., where \(b < r < c\). - *Hint*: This was one of the [Test 2 Review problems.](#). Remember, derive the answer independently. (d) **Outside the Cable**: Find the magnetic field where \(r > c\).
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