Problem 1

Two media are separated by a planar boundary which is marked as xy plane.

Both media are perfect and nonmagnetic dielectrics with a dielectric constant

€r1 = 2.25 in medium 1 and 2 = 4 in medium 2. In medium 1 there is a plane

wave with its electric field described as

E¹ = 28 cos (67 × 108 t - 30m z)

(V/m)

The field is a traveling wave in medium 1. It is incident on the boundary,

indicated by the super index.

1. Make a sketch to show the media, the boundary, the field E¹, the associated

field H', the direction of the wave propagation, and the wave front.

2. Find the phase difference in radians per meter between two wave fronts of

this propagating wave in medium 1.

3. Find the time-domain expression of the field H¹.

4. Find the impedance of medium 1 and that of medium 2. Use them to

compute the reflection coefficient I and the transmission coefficient 7.

5. Find the time-domain expressions of the fields of the reflected wave and

the fields of the transmitted wave. You may use phasors to do the com-

putation. Add to the sketch to indicate the direction of the fields of the

reflected and transmitted waves and the direction they propagate.

6. Determine the time-average power densities of the incident, reflected, and

transmitted waves.