he magnetic field H for both r

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...
icon
Related questions
icon
Concept explainers
Question

My question is under attachment.

### 2nd Question:

For the same coaxial cable of the previous question, now carrying a uniformly distributed current \(I\), find the following. Assume permeability of free space in all regions.

1. The magnetic field \(H\) for both \(r < a\) and \(a < r < b\).

2. The "external" inductance per unit of length corresponding to the magnetic field in the region \(a < r < b\).

3. The internal inductance per unit of length corresponding to the magnetic field inside the interior conductor. Comment on your result.

**Hint:** Use the internal magnetic field found in (1) to calculate the magnetic energy density. Then integrate that to find the total energy inside the conductor per unit of length. Use the relationship between energy stored and inductance to find the value of the inductance.
Transcribed Image Text:### 2nd Question: For the same coaxial cable of the previous question, now carrying a uniformly distributed current \(I\), find the following. Assume permeability of free space in all regions. 1. The magnetic field \(H\) for both \(r < a\) and \(a < r < b\). 2. The "external" inductance per unit of length corresponding to the magnetic field in the region \(a < r < b\). 3. The internal inductance per unit of length corresponding to the magnetic field inside the interior conductor. Comment on your result. **Hint:** Use the internal magnetic field found in (1) to calculate the magnetic energy density. Then integrate that to find the total energy inside the conductor per unit of length. Use the relationship between energy stored and inductance to find the value of the inductance.
1st Question:

A coaxial cable consists of an internal solid cylindrical conductor of radius \(a\) and a cylindrical conductive shell of radius \(b\) separated by a dielectric of permittivity \(\varepsilon\). Assuming the length of the cable as infinite and that it carries an electric charge of \(q_1\) coulombs/meter, find the following:

1. The electric field \(E\) for \(a < r < b\)

   *Note: \(r\) is the cylindrical radius.*

2. The voltage difference between the two conductor surfaces.

3. The voltage \(V(a)\), assuming \(V(b) = 0\).

4. Since the maximum value of the electric field occurs at the surface \(r = a\), and that value cannot exceed the value \(E_{\text{max}}\) that causes the dielectric breakdown, find the relation between \(a\) and \(b\) that makes the potential difference between the conductors the maximum possible.

   *Hint: Use the expressions of \(E\) and \(V\) found in (1) to (3) to relate \(V(a)\) and \(E(a)\), therefore eliminating \(q_1\) from the equations. Then find the maximum of \(V(a)\) as a function of \(a\), with \(E(a) = E_{\text{max}}\) and \(b\) constant.*

5. Assuming that the dielectric breakdown occurs for \(E_{\text{max}} = 10 \text{ kvolts/cm}\), and that \(a = 0.1 \text{cm}\), find the maximum voltage the cable can carry.
Transcribed Image Text:1st Question: A coaxial cable consists of an internal solid cylindrical conductor of radius \(a\) and a cylindrical conductive shell of radius \(b\) separated by a dielectric of permittivity \(\varepsilon\). Assuming the length of the cable as infinite and that it carries an electric charge of \(q_1\) coulombs/meter, find the following: 1. The electric field \(E\) for \(a < r < b\) *Note: \(r\) is the cylindrical radius.* 2. The voltage difference between the two conductor surfaces. 3. The voltage \(V(a)\), assuming \(V(b) = 0\). 4. Since the maximum value of the electric field occurs at the surface \(r = a\), and that value cannot exceed the value \(E_{\text{max}}\) that causes the dielectric breakdown, find the relation between \(a\) and \(b\) that makes the potential difference between the conductors the maximum possible. *Hint: Use the expressions of \(E\) and \(V\) found in (1) to (3) to relate \(V(a)\) and \(E(a)\), therefore eliminating \(q_1\) from the equations. Then find the maximum of \(V(a)\) as a function of \(a\), with \(E(a) = E_{\text{max}}\) and \(b\) constant.* 5. Assuming that the dielectric breakdown occurs for \(E_{\text{max}} = 10 \text{ kvolts/cm}\), and that \(a = 0.1 \text{cm}\), find the maximum voltage the cable can carry.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
8085 Microprocessor
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,