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**Unformatted text preview: **ECE 222B Midterm Exam February 11th, 2010 Instructions. This is an 80 minute, closed book, examination. Calculators are not permitted. 1. (20 points) Assume that the electric field of a time-harmonic wave in a vacuum takes the form ~ E = ~ E exp h- j ~ ~ r i where ~ = ~ r- j ~ i , and where ~ E , ~ r , and ~ i are all real vector constants. Prove that if both ~ r and ~ i are non-zero, then ~ i ~ r = 0. 2. (20 points) Assume that a TEM z wave propagates in a vacuum with frequency . Defining 2 = 2 x 2 + 2 y 2 prove that 2 H = 0 and that 2 H z 2 = 2 H t 2 Hint: Do the proof using a cartesian coordinate system and the Maxwell equations. 3. Assume that in the region z > 0 you are given a homogeneous, isotropic medium with constant permittivity . Assume that this medium is bounded by a vacuum at z = 0 (see Figure). A time-harmonic, parallel polarized wave ( H field has y-component only) of frequency is incident on the surface from the vacuum side of the boundary ( z < 0), and propagates at an angle i with respect to the normal of the surface....

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