Problem 8.5 Consider an infinite parallel-plate capacitor, with the lower plate (at z = -d/2) carrying the charge density -o, and the upper plate (at z = +d/2) carrying the charge density +o. (a) Determine all nine elements of the stress tensor, in the region between the plates. Display your answer as a 3 x 3 matrix: Txx Txy Tx2 Тух Tyy Tyz Tex Tzy T2z (b) Use Eq. 8.22 to determine the force per unit area on the top plate. Compare Eq. 2.51. (c) What is the momentum per unit area, per unit time, crossing the xy plane (or any other plane parallel to that one, between the plates)? (d) At the plates this momentum is absorbed, and the plates recoil (unless there is some nonelectrical force holding them in position). Find the recoil force per unit area on the top plate, and compare your answer to (b). [Note: This is not an additional force, but rather an alternative way of calculating the same force-in (b) we got it from the force law, and in (d) we did it by conservation of momentum.]

Problem 8.5 Consider an infinite parallel-plate capacitor, with the lower plate (at z = -d/2) carrying the charge density -o, and the upper plate (at z = +d/2) carrying the charge density +o. (a) Determine all nine elements of the stress tensor, in the region between the plates. Display your answer as a 3 x 3 matrix: Txx Txy Tx2 Тух Tyy Tyz Tex Tzy T2z (b) Use Eq. 8.22 to determine the force per unit area on the top plate. Compare Eq. 2.51. (c) What is the momentum per unit area, per unit time, crossing the xy plane (or any other plane parallel to that one, between the plates)? (d) At the plates this momentum is absorbed, and the plates recoil (unless there is some nonelectrical force holding them in position). Find the recoil force per unit area on the top plate, and compare your answer to (b). [Note: This is not an additional force, but rather an alternative way of calculating the same force-in (b) we got it from the force law, and in (d) we did it by conservation of momentum.]

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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Question

Problem 8.5 Consider an infinite parallel-plate capacitor, with the lower plate (at z = -d/2)
carrying the charge density -o, and the upper plate (at z = +d/2) carrying the charge density
+o.
(a) Determine all nine elements of the stress tensor, in the region between the plates. Display
your answer as a 3 x 3 matrix:
Txx Txy Txz
Тух Туу Туг
Tzx
Tzy Tzz
(b) Use Eq. 8.22 to determine the force per unit area on the top plate. Compare Eq. 2.51.
(c) What is the momentum per unit area, per unit time, crossing the xy plane (or any other
plane parallel to that one, between the plates)?
(d) At the plates this momentum is absorbed, and the plates recoil (unless there is some
nonelectrical force holding them in position). Find the recoil force per unit area on the top
plate, and compare your answer to (b). [Note: This is not an additional force, but rather an
alternative way of calculating the same force-in (b) we got it from the force law, and in (d)
we did it by conservation of momentum.]
A

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