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Unformatted text preview: EEE 445 Homework #1 Solutions 1.1 Assume that an infinite sheet of electric surface current density x J J s ˆ A/m is placed on the z = 0 plane between free-space for z < 0, and a dielectric with r for z > 0, as shown below. Find the resulting E and H fields in the two regions. HINT: Assume plane wave solutions propagating away from the current sheet, and match boundary conditions to find the amplitudes, as in Example 1.3. Solution: For region 1 ( z <0 ), we have 1 1 k k For region 2 ( z > 0), we have 2 2 k k r r Following Example 1.3, we assume for z <0, z jk z jk Ae y H e A x E ˆ ˆ 1 1 and for z > 0, 2 2 ˆ ˆ r r j k z r j k z E x B e H y B e The boundary conditions at z = 0 are: (1) ˆ 1 2 E E z , or A B B A r r (2) x J H H z ˆ ˆ 1 2 , or J A B Solving for A and B , we obtain 1 1 r r r J B J A Notice that for 1 r , we reproduce the solution of Example 2.3. 1.9 Consider a plane wave propagating in a lossy dielectric medium for z < 0, with a perfectly conducting plate at z = 0. Assume that the lossy medium is characterized by 2 5 j , , and that the frequency of the plane wave is 1.0 GHz, and let the amplitude of the incident electric field be 4 V/m at z = 0. Find the reflected electric field for z < 0, and plot the magnitude of the total electric field for 5 . z ....
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This note was uploaded on 12/14/2010 for the course EEE 445 taught by Professor Georgepan during the Fall '10 term at ASU.
- Fall '10