Consider an infinite parallel-plate capacitor, with the lower plate (at z = ?? d/2) carrying the charge density -a, and the upper plate (at z = +d/2) carrying the charge density

(a) Determine all nine elements of the stress tensor, in the region between the plates. Display your answer as a 3 x 3 matrix:

(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 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.]

Transcribed Image Text:

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