312ps5 - PROBLEM SET 5 ECE 312 Autumn Quarter 2010...

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PROBLEM SET 5 ECE 312 Autumn Quarter 2010 Assigned: October 27th Due: November 3rd in class Instructor: Joel Johnson Problem 1 Two plane waves in free space are given by E ˜ 1 x ˆ j 2 y ˆ () e jkz = (V/m), and E ˜ 2 2 j + y ˆ e = (V/m). (a) What is the time average Poynting vector associated with E ˜ 1 alone? (b) What is the time average Poynting vector associated with E ˜ 2 alone? (c) What is the time average Poynting vector associated with the field E ˜ E ˜ 1 E ˜ 2 + = Is this equal to the sum of your part (a) and (b) answers? (d) Now let the field E ˜ 2 be set to zero. How many Watts of time average power radiated by the field E ˜ 1 are intercepted by a circular spot of radius 20 cm in the x-y plane? Problem 2 A 1900 MHz cellular phone user is talking inside of a building. Assume that the phone gener- ates an electromagnetic wave E ˜ i x ˆ e jk 1 z = (V/m) that impinges from free space (medium 1) inside the building onto a wall of the buidling (medium 2, ε 2 5.4 ε 0 = , μ 2 μ 0 = , and σ 2 0.04 = S/m) at normal incidence. Consider the wall to be very thick, and to exist for z 0 > . (a) Find the complex reflection coefficient.
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