PROBLEM SET 5ECE 312 Autumn Quarter 2010Assigned:October 27thDue:November 3rd in classInstructor: Joel JohnsonProblem 1Two plane waves in free space are given by E˜1xˆj2yˆ–()ejkz=(V/m), and E˜22j+yˆe=(V/m).(a) What is the time average Poynting vector associated with E˜1alone?(b) What is the time average Poynting vector associated with E˜2alone?(c) What is the time average Poynting vector associated with the field E˜E˜1E˜2+=Is this equal to the sum of your part (a) and (b) answers?(d) Now let the field E˜2be set to zero. How many Watts of time average power radiated by the field E˜1are intercepted by a circular spot of radius 20 cm in the x-y plane?Problem 2A 1900 MHz cellular phone user is talking inside of a building. Assume that the phone gener-ates an electromagnetic wave E˜ixˆejk1z–=(V/m) that impinges from free space (medium 1) inside the building onto a wall of the buidling (medium 2, ε25.4ε0=, μ2μ0=, and σ20.04=S/m) at normal incidence. Consider the wall to be very thick, and to exist for z0>.(a) Find the complex reflection coefficient.
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