### Understanding the Magnetic Field in a Coaxial CableA 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 ExplanationThe 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 StatementUse 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 \(r > c\).

According to Ampere's law, integral of the magnetic field intensity over a closed path is equal to…

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)

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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Concept explainers

HVDC

HVDC stands for high voltage direct current in the electric power transmission system. The high voltage direct current system uses direct current (DC) for the transmission of electrical power through transmission lines in contrast with the alternating current that is the AC system. The HVDC is used to transmit bulk power point-to-point through long distances transmission lines. Power is rapidly transferred because the efficiency of transmission lines is greatly increased over long distances due to HVDC lines.

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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 \(r > c\).

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