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
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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 acreb.
2. The "external" inductance per unit of length corresponding to the magnetic field in the region acreb.
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 unity 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 acreb. 2. The "external" inductance per unit of length corresponding to the magnetic field in the region acreb. 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 unity 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 e. Assuming the length of the cable as infinite and
that it carries an electric charge of q 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 can not exceed
the value Emax that causes the dielectric breakdown, find the relation between a and b that nes 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, from
the equations. Then find the maximum of V(a) as function of a, with E(a) = Emax and b constant.
5. Assuming that the dielectric breakdown occurs for Emax =10 kvolts/cm, and that a= 0.1cm, 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 e. Assuming the length of the cable as infinite and that it carries an electric charge of q 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 can not exceed the value Emax that causes the dielectric breakdown, find the relation between a and b that nes 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, from the equations. Then find the maximum of V(a) as function of a, with E(a) = Emax and b constant. 5. Assuming that the dielectric breakdown occurs for Emax =10 kvolts/cm, and that a= 0.1cm, find the maximum voltage the cable can carry.
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